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{{short description|Spherical shell structure based on a geodesic polyhedron}}
{{Refimprove|date=April 2010}}
{{More citations needed|date=April 2010}}
[[File:Epcot07.jpg|thumb|[[Spaceship Earth (Epcot)|Spaceship Earth]] at [[Epcot]], [[Walt Disney World]], a geodesic sphere]]
[[File:Mtl. Biosphere in Sept. 2004.jpg|thumb|upright=1.7|The [[Montreal Biosphère]], formerly the American Pavilion of [[Expo 67]], by [[Buckminster Fuller|R. Buckminster Fuller]], on [[Île Sainte-Hélène]], [[Montreal]], [[Quebec]]]]
B '''geodesic dome''' is a spherical or partial-spherical [[thin-shell structure|shell structure or lattice shell]] based on a network of [[great circle]]s ([[geodesic]]s) lying on the surface of a [[sphere]]. The geodesics intersect to form [[triangular]] elements that have local triangular rigidity and also distribute the [[stress (physics)|stress]] across the entire structure. When completed to form a complete sphere, it is known as a '''geodesic sphere'''. The term "dome" refers to an enclosed structure and should not be confused with non-enclosed geodesic structures such as geodesic climbers found on playgrounds.
A '''geodesic dome''' is a [[hemispherical]] [[thin-shell structure]] (lattice-shell) based on a [[geodesic polyhedron]]. The [[Structural rigidity|rigid]] [[triangular]] elements of the dome distribute [[Stress (mechanics)|stress]] throughout the structure, making geodesic domes able to withstand very heavy [[Structural load|loads]] for their size.


==History==
Typically the design of a geodesic dome begins with an [[icosahedron]] inscribed in a sphere, tiling each triangular face with smaller triangles, then projecting the vertices of each tile to the sphere.
[[File:Epcot07.jpg|thumb|[[Spaceship Earth (Epcot)|Spaceship Earth]] at [[Epcot]]]]
The endpoints of the links of the completed sphere would then be the projected endpoints on the sphere's surface. If this is done exactly, each of the edges of the sub-triangles is a slightly different length, so it would require a very large number of links of different sizes.
[[File:Climatron, Missouri Botanical Gardens.jpg|thumb|[[Climatron|The Climatron]] greenhouse at [[Missouri Botanical Gardens]], built in 1960 and designed by Thomas C. Howard of Synergetics, Inc., inspired the domes in the science fiction movie ''[[Silent Running]]''.]]
To minimize the number of different sizes of links, various simplifications are made. The result is a compromise consisting of a pattern of triangles with their vertices lying approximately on the surface of the sphere. The edges of the triangles form approximate geodesic paths over the surface of the dome that distribute its weight.
[[File:Science World at TELUS World of Science.jpg|alt=Science World in Vancouver|thumb|[[Science World (Vancouver)|Science World]] in Vancouver, built for [[Expo 86]], and inspired by Buckminster Fuller's Geodesic dome.]]
[[File:Rise_Belfast.png|thumb|[[RISE (sculpture)|RISE]], public art designed by [[Wolfgang Buttress]], located in [[Belfast]], consists of two spheres which utilise Buckminster Fuller's Geodesic dome.]]
The first geodesic dome was designed after [[World War I]] by [[Walther Bauersfeld]],<ref>[http://www.physics.princeton.edu/~trothman/domes.html First Geodesic Dome: Planetarium in Jena 1922] incl. patent information {{webarchive |url=https://web.archive.org/web/20130319084511/http://www.physics.princeton.edu/~trothman/domes.html |date=March 19, 2013 }}</ref> chief engineer of [[Carl Zeiss AG|Carl Zeiss Jena]], an optical company, for a [[planetarium]] to house his planetarium projector. An initial, small dome was patented and constructed by the firm of Dykerhoff and Wydmann on the roof of the Carl Zeiss Werke in [[Jena]], [[Germany]]. A larger dome, called "The Wonder of Jena", opened to the public in July 1926.<ref>{{cite web |url=http://www.planetarium-jena.de/Geschichte.43.0.html |title=Zeiss-Planetarium Jena: Geschichte |publisher=Planetarium-jena.de |access-date=2015-08-30 |archive-url=https://web.archive.org/web/20150831010729/http://www.planetarium-jena.de/Geschichte.43.0.html |archive-date=2015-08-31 |url-status=dead }}</ref>


Twenty years later, [[Buckminster Fuller]] coined the term "geodesic" from field experiments with artist [[Kenneth Snelson]] at [[Black Mountain College]] in 1948 and 1949. Although Fuller was not the original inventor, he is credited with the U.S. popularization of the idea for which he received {{US patent|2682235A}} on 29 June 1954.<ref>For a more detailed historical account, see the chapter "Geodesics, Domes, and Spacetime" in Tony Rothman's book ''Science à la Mode'', Princeton University Press, 1989.</ref> The oldest surviving dome built by Fuller himself is located in [[Woods Hole, Massachusetts]], and was built by students under his tutelage over three weeks in 1953.<ref>{{cite web|url=https://www.domewoodshole.org/|title=The Woods Hole Dome|access-date=2019-07-02|archive-url=https://web.archive.org/web/20190702153452/https://www.domewoodshole.org/ |archive-date=2 July 2019}}</ref>
Geodesic designs can be used to form any curved, enclosed space. Oddly-shaped designs would require calculating for and custom building of each individual strut, vertex or panel—resulting in potentially expensive construction. Because of the expense and complexity of design and fabrication of any geodesic dome, builders have tended to standardize using a few basic designs.


The geodesic dome appealed to Fuller because it was extremely strong for its weight, its "omnitriangulated" surface provided an inherently stable structure, and because a sphere encloses the greatest volume for the least surface area.
==Related patterns==
Similar geodesic structures may be based upon the pattern of edges and vertices of certain [[platonic solid]]s, or upon various expansions of these called [[Johnson solid]]s. Such structures may be composed of struts of uniform length while having faces other than triangles such as pentagons or squares, or these faces may be subdivided by struts of other than the basic length. Plans and licenses for such structures derived from licenses of the Fuller patents were produced during the 1970s by [[Zomeworks]] (now a manufacturer of [[solar tracker]]s). Both geodesic and non-geodesic structures can be derived similarly from the [[archimedean solid]]s and [[catalan solid]]s.


The dome was successfully adopted for specialized uses, such as the 21 [[Distant Early Warning Line]] domes built in Canada in 1956,<ref>{{cite web |url=http://www.bernardkirschenbaum.com/Bernard_Kirschenbaum/audio.html |title=Audio interview with Bernard Kirschenbaum on DEW Line domes |publisher=Bernardkirschenbaum.com |access-date=2010-10-17 |archive-date=2011-04-20 |archive-url=https://web.archive.org/web/20110420071723/http://www.bernardkirschenbaum.com/Bernard_Kirschenbaum/audio.html |url-status=dead }}</ref> the 1958 [[Union Tank Car Company]] dome near [[Baton Rouge, Louisiana]], designed by Thomas C. Howard of Synergetics, Inc. and specialty buildings such as the [[Henry J. Kaiser|Kaiser Aluminum]] domes (constructed in numerous locations across the US, e.g., [[Virginia Beach, Virginia]]), auditoriums, weather observatories, and storage facilities. The dome was soon breaking records for covered surface, enclosed volume, and construction speed.
The building of strong stable structures out of patterns of reinforcing triangles<!-- WRONG! , called [[tensegrity]],--> is most commonly seen in [[tent]] design. It has been applied in the abstract in other [[industrial design]], but even in [[management science]] and deliberative [[structure]]s as a [[conceptual metaphor]], especially in the work of [[Stafford Beer]], whose ''transmigration'' method is based so specifically on dome design that only fixed numbers of people can take part in the process at each [[deliberation]] stage.


Beginning in 1954, the U.S. Marines experimented with [[helicopter]]-deliverable geodesic domes. A 30-foot wood and plastic geodesic dome was lifted and carried by helicopter at 50 knots without damage, leading to the manufacture of a standard magnesium dome by Magnesium Products of Milwaukee. Tests included assembly practices in which previously untrained Marines were able to assemble a 30-foot magnesium dome in 135 minutes, helicopter lifts off aircraft carriers, and a durability test in which an anchored dome successfully withstood without damage, a day-long {{convert|120|mph|abbr=on}} propeller blast from the twin 3,000 horsepower engines of an anchored airplane.<ref>{{cite book |last1=Fuller |last2=Marks |first1= R. Buckminster |first2=Robert |date=1973 |title=The Dymaxion World of Buckminster Fuller |publisher=Anchor Books |page=203 |isbn=0-385-01804-5}}</ref>
== History ==
[[File:Mtl. Biosphere in Sept. 2004.jpg|right|thumb|The [[Montreal Biosphère]], formerly the American Pavilion of [[Expo 67]], by [[R. Buckminster Fuller]], on [[Île Sainte-Hélène]], [[Montreal]], [[Canada]]]]


The 1958 [[Gold Dome]] in Oklahoma City, Oklahoma, utilized Fuller's design for use as a bank building. Another early example was the [[Stepan Center]] at the [[University of Notre Dame]], built in 1962.<ref>{{cite web |last1=Archives |first1=Notre Dame |title=Mid-Century Modern |url=http://www.archives.nd.edu/about/news/index.php/2010/mid-century-modern/ |website=Notre Dame Archives News & Notes |access-date=15 July 2019 |date=17 September 2010}}</ref>
The first dome that could be called "geodesic" in every respect was designed just after [[World War I]] by [[Walther Bauersfeld]],<ref>[http://www.physics.princeton.edu/~trothman/domes.html First Geodesic Dome: Planetarium in Jena 1922] incl. patent information</ref> chief engineer of the [[Carl Zeiss]] optical company, for a [[planetarium]] to house his new planetarium projector. The dome was patented, constructed by the firm of Dykerhoff and Wydmann on the roof of the Zeiss plant in [[Jena]], [[Germany]], and opened to the public in July 1926.<ref>according to http://www.planetarium-jena.de/Geschichte.43.0.html</ref> Some 30 years later, [[Buckminster Fuller|R. Buckminster Fuller]] named the dome "geodesic" from field experiments with artist [[Kenneth Snelson]] at [[Black Mountain College]] in 1948 and 1949. Snelson and Fuller worked together in developing what they termed "tensegrity," an engineering principle of continuous tension and discontinuous compression that allowed domes to deploy a lightweight lattice of interlocking icosahedrons that could be skinned with a protective cover. Although Fuller was not the original inventor, he developed the intrinsic mathematics of the dome, thereby allowing popularization of the idea &mdash; for which he received a U.S. patent in 1954.<ref>For a more detailed historical account, see the chapter "Geodesics, Domes, and Spacetime" in Tony Rothman's book "Science a la Mode", Princeton University Press, 1989.</ref>


The dome was introduced to a wider audience as [[1964 New York World's Fair pavilions#Other pavilions|a pavilion]] for the [[1964 New York World's Fair]] designed by Thomas C. Howard of Synergetics, Inc. This dome is now used as an [[aviary]] by the [[Queens Zoo]] in [[Flushing Meadows Corona Park]].<ref name="nyt-1993-01-03">{{Cite news |last=Gray |first=Christopher |date=1993-01-03 |title=Streetscapes: The Queens Aviary; A Great Outside Interior Space |url=https://www.nytimes.com/1993/01/03/realestate/streetscapes-the-queens-aviary-a-great-outside-interior-space.html |access-date=2024-06-01 |work=The New York Times |language=en-US |issn=0362-4331}}</ref>
The geodesic dome appealed to Fuller because it was extremely strong for its weight, its "omnitriangulated" surface provided an inherently stable structure, and because a sphere encloses the greatest volume for the least surface area. Fuller hoped that the geodesic dome would help address the postwar housing crisis. This was consistent with his prior hopes for both versions of the [[Dymaxion House]].


Another dome is from [[Expo 67]] at the [[Montreal]] World's Fair, where it was part of the American Pavilion. The structure's covering later burned, but the structure itself still stands and, under the name [[Montréal Biosphère|Biosphère]], currently houses an interpretive [[museum]] about the [[Saint Lawrence River]].
[[File:Climatron, Missouri Botanical Gardens.jpg|thumb|[[Climatron|The Climatron]] greenhouse at [[Missouri Botanical Gardens]], built during 1960, inspired the domes in the science fiction movie ''[[Silent Running]].'']]


In the 1970s, [[Zomeworks]] licensed plans for structures based on other geometric solids, such as the [[Johnson solid]]s, [[Archimedean solid]]s, and [[Catalan solid]]s.<ref>Geodesic domes are most often based on [[Platonic solid]]s, particularly the [[icosahedron]].</ref> These structures may have some faces that are not triangular, being squares or other polygons.
However, from a practical perspective, geodesic constructions have some disadvantages. They have a very large number of edges in comparison with more conventional structures which have just a few large flat surfaces. Each of the edges must be prevented from leaking, which can be quite challenging for a geodesic structure. Also, spaces enclosed within curved boundaries tend to be less usable than spaces enclosed within flat boundaries. (Since it would be impractical to produce sofas with every possible curved shape, they are normally constructed along straight lines, and so leave wasted space when placed in a curved space.)


In 1975, a dome was constructed at the [[Amundsen–Scott South Pole Station|South Pole]], where its resistance to snow and wind loads was important.
The dome was successfully adopted for specialized industrial use, such as the 1958 [[Union Tank Car Company]] dome near [[Baton Rouge, Louisiana]] and specialty buildings like the [[Henry Kaiser|Kaiser Aluminum]] domes (constructed in numerous locations across the US, e.g., [[Virginia Beach, Virginia|Virginia Beach, VA]]), auditoriums, weather observatories, and storage facilities. The dome was soon breaking records for covered surface, enclosed volume, and construction speed. According to a WAFB-TV of [[Baton Rouge]] news report on November 27, 2007, the Union Tank Car Company Dome has been demolished.


On October 1, 1982, one of the most famous geodesic domes, [[Spaceship Earth (Epcot)|Spaceship Earth]] at [[Epcot]] in [[Walt Disney World Resort]] in [[Bay Lake, Florida|Bay Lake]], [[Florida]], just outside of [[Orlando, Florida|Orlando]] opened. The building and the ride inside of it are named with one of Buckminster Fuller's famous terms, [[Spaceship Earth]], a world view expressing concern over the use of limited resources available on Earth and encouraging everyone on it to act as a harmonious crew working toward the greater good. The building is Epcot's icon, representing the entire park.
Leveraging the geodesic dome's stability, the US Air Force experimented with [[helicopter]]-deliverable units.


For the [[Expo 86|1986 World's Fair (Expo 86)]], held in [[Vancouver]], a Buckminster Fuller-inspired Geodesic dome was designed by the Expo's chief architect [[Bruno Freschi]] to serve as the fair's Expo Centre. Construction began in 1984 and was completed by early 1985. The dome and the building now serve as an Arts, Science and Technology center, and has been named [[Science World (Vancouver)|Science World]].<ref>[http://www.scienceworld.ca/whats_on/omnimax_theatre/omnifacts.htm Science World – OMNIMAX Theatre – OMNIMAX Facts<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20060626233923/http://www.scienceworld.ca/whats_on/omnimax_theatre/omnifacts.htm|date=2006-06-26}}</ref>
The dome was introduced to a wider audience as a pavilion for the 1964 [[World's Fair]] in [[New York City]]. This dome is now used as an [[aviary]] by the [[Queens Zoo]] in Flushing Meadows Corona Park.


In 2000, the world's first fully sustainable geodesic dome hotel, EcoCamp Patagonia, was built at
Another dome is from [[Expo 67]] the [[Montreal, Canada]] [[World's Fair]] as part of the American Pavilion. The structure's covering later burned, but the structure itself still stands and, under the name ''[[Montreal Biosphère|Biosphère]],'' currently houses an interpretive [[museum]] about the [[Saint Lawrence River]].
[[Kawésqar National Park]] in [[Chile]]an [[Patagonia]],<ref>{{cite web |url=http://www.domerama.com/ecocamp-the-worlds-first-geodesic-dome-hotel/ |title=EcoCamp, the world's first geodesic dome hotel |website=domerama.com |access-date=2 February 2022 |archive-url=https://archive.today/20130215212310/http://www.domerama.com/ecocamp-the-worlds-first-geodesic-dome-hotel/ |archive-date=15 February 2013 |url-status=dead}}</ref> opening the following year in 2001. The hotel's dome design is key to resisting the region's strong winds and is based on the dwellings of the indigenous [[Alacalufe people|Kaweskar people]]. Geodomes are also becoming popular as a [[glamping]] (glamorous camping) unit.


==Methods of construction==
During the 1970s, the [[Cinesphere]] dome was built at the [[Ontario Place]] amusement park in [[Toronto]], [[Canada]]. During 1975, a dome was constructed at the [[Amundsen-Scott South Pole Station|South Pole]], where its resistance to snow and wind loads is important.
[[File:Long Island Green Dome.jpg|thumb|Long Island Green Dome]]
Wooden domes have a hole drilled in the width of a [[strut]]. A stainless steel band locks the strut's hole to a steel pipe. With this method, the struts may be cut to the exact length needed. Triangles of exterior plywood are then nailed to the struts. The dome is wrapped from the bottom to the top with several stapled layers of [[tar paper]], to shed water, and finished with shingles. This type of dome is often called a hub-and-strut dome because of the use of steel hubs to tie the struts together.


Paneled domes are constructed of separately framed timbers covered in plywood. The three members comprising the triangular frame are often cut at compound angles to provide for a flat fitting of the various triangles. Holes are drilled through the members at precise locations and steel bolts then connect the triangles to form the dome. These members are often 2x4s or 2x6s, which allow for more [[Building insulation|insulation]] to fit within the triangle. The panelized technique allows the builder to attach the plywood skin to the triangles while safely working on the ground or in a comfortable shop out of the weather. This method does not require expensive steel hubs.
Residential geodesic domes have been less successful than those used for working and/or entertainment, largely because of their complexity and consequent greater construction costs. Fuller himself lived in a geodesic dome in [[Carbondale, Illinois]], at the corner of Forest and Cherry [http://maps.google.com/maps?f=q&source=s_q&hl=en&geocode=&q=Carbondale,+Illinois,Forest+and+Cherry&sll=37.727097,-89.218617&sspn=0.157225,0.304871&g=Carbondale,+Illinois,&ie=UTF8&ll=37.722885,-89.225507&spn=0.002355,0.004764&t=h&z=18&iwloc=A&layer=c&cbll=37.722766,-89.22551&panoid=AaNkKvIMPGlPFAOFvTFv6w&cbp=12,26.827702702702687,,0,-2.813555743243249]. Residential domes have not become as popular as Fuller hoped.
He thought of residential domes as air-deliverable products manufactured by an aerospace-like industry. Fuller's dome home still exists, and a group called RBF Dome NFP is attempting to restore the dome and have it registered as a National Historic Landmark.


Steel framework can be easily constructed of electrical conduit. One flattens the end of a strut and drills bolt holes at the needed length. A single bolt secures a vertex of struts. The nuts are usually set with removable locking compound, or if the dome is portable, have a [[castellated nut]] with a [[Cotter (pin)|cotter pin]]. This is the standard way to construct domes for [[jungle gym]]s.
==Chord factors==
{| class="wikitable" style="float:right;margin: 0em 0em 1em 1em" <!-- is this the preferred way to make some margin? -->
|style="padding:0.5em;text-align:center;"|
[[Image:Géode V 3 1.gif]] [[Image:Géode V 3 1 duale.gif]]<br />
A geodesic sphere and its [[Dual polyhedron|dual]].
|}


Domes can also be constructed with a lightweight aluminium framework which can either be bolted or welded together or can be connected with a more flexible nodal point/hub connection. These domes are usually clad with glass which is held in place with a PVC [[Coping (architecture)|coping]], which can be sealed with silicone to make it watertight. Some designs allow for double glazing or for insulated panels to be fixed in the framework.
The mathematical object "chord" of the "geodesic sphere" corresponds to the structural "strut" of the physical "geodesic dome". The general definition of a [[chord (geometry)|chord]] is a (straight) line segment joining two points on a curve. For simple geodesic domes we recognize the associated curve to be the surface of a sphere. Here is how chords of geodesic spheres are generated. We first choose an underlying [[polyhedron]] with equal triangle faces. The regular [[icosahedron]] is most popular. The sphere we use is specifically the "circumscribing sphere" that contains the points (vertices) of the underlying polyhedron. The desired '''frequency''' of the subsequent geodesic sphere or dome is the number of parts or segments into which a side (edge) of the underlying polyhedral triangle is subdivided. The frequency has historically been denoted by the Greek letter "ν" (''[[nu (letter)|nu]]''). By connecting like points along the subdivided sides we produce a natural triangular grid of segments inside each underlying triangle face. Each segment of the grid is then projected as a "chord" onto the surface of the circumscribing sphere. The technical definition of a '''chord factor''' is the ratio of the chord length to the radius of the circumscribing sphere. It is therefore convenient to think of the circumscribing sphere as scaled to radius = 1 in which "chord factors" are the same as "chord lengths" (decimal numbers less than one).


Concrete and foam-plastic domes generally start with a steel framework dome, wrapped with chicken wire and wire screen for reinforcement. The [[chicken wire]] and screen are tied to the framework with wire ties. A coat of material is then sprayed or molded onto the frame. Tests should be performed with small squares to achieve the correct consistency of concrete or plastic. Generally, several coats are necessary on the inside and outside. The last step is to saturate concrete or polyester domes with a thin layer of [[epoxy]] compound to shed water.
For geodesic spheres a well-known formula for calculating any "chord factor" is


Some concrete domes have been constructed from prefabricated, prestressed, steel-reinforced concrete panels that can be bolted into place. The bolts are within raised receptacles covered with little concrete caps to shed water. The triangles overlap to shed water. The triangles in this method can be molded in forms patterned in sand with wooden patterns, but the concrete triangles are usually so heavy that they must be placed with a crane. This construction is well-suited to domes because no place allows water to pool on the concrete and leak through. The metal fasteners, joints, and internal steel frames remain dry, preventing frost and corrosion damage. The concrete resists sun and weathering. Some form of internal flashing or caulking must be placed over the joints to prevent drafts. The 1963 [[Cinerama Dome]] was built from [[precast concrete]] hexagons and pentagons.
'''chord factor = 2 Sin (θ / 2)'''
where '''θ''' is the corresponding angle of arc for the given chord, that is, the "central angle" spanned by the chord with respect to the center of the circumscribing sphere. Determining the central angle usually requires some non-trivial [[spherical geometry]].


Domes can now be printed at high speeds using very large, mobile "3D Printers", also known as additive manufacturing machines. The material used as the filament is often a form of air injected concrete or closed-cell plastic foam.
[[File:Eden project tropical biome.jpg|thumb|Inside the [[Eden Project]] tropical [[biome]]]]


In ''Geodesic Math and How to Use It'' [[Hugh Kenner]] writes, "Tables of chord factors, containing as they do the essential design information for spherical systems, were for many years guarded like military secrets. As late as 1966, some 3''ν'' icosa figures from ''[[Popular Science (magazine)|Popular Science Monthly]]'' were all anyone outside the circle of Fuller licensees had to go on." (page 57, 1976 edition). Other tables became available with publication of Lloyd Kahn's ''Domebook 1'' (1970) and ''Domebook 2'' (1971). With advent of personal computers, the mathematics became more solvable. Rick Bono's '''Dome''' software outputs a script that can be used with the [[POV-ray]] [[Ray tracing (graphics)|raytrace]] to produce 3D pictures of domes. Domes based on the frameworks of different underlying polyhedra along with various methods for subdividing them will produce quite different results. Mathematical formulas developed by Peter W. Messer for calculating chord factors and [[dihedral angles]] for the general geodesic sphere appear in the Appendix of the 1999 Dover edition of [http://www.employees.csbsju.edu/mwenninger/magnus2000.html Spherical Models] by [[Magnus J. Wenninger]].
Given the complicated geometry of the geodesic dome, dome builders rely on tables of strut lengths, or "chord factors". In ''Geodesic Math and How to Use It'', [[Hugh Kenner]] wrote, "Tables of chord factors, containing as they do the essential design information for spherical systems, were for many years guarded like military secrets. As late as 1966, some 3''ν'' icosa figures from ''[[Popular Science (magazine)|Popular Science Monthly]]'' were all anyone outside the circle of Fuller licensees had to go on." (page 57, 1976 edition). Other tables became available with publication of Lloyd Kahn's ''Domebook 1'' (1970) and ''Domebook 2'' (1971).
<br style="clear:right;" />
==Methods of construction==
[[File:Vitra geodesic dome tubing.jpg|thumb|Construction details of a permanently installed tent-type geodesic dome by [[Buckminster Fuller]].]]
Wooden domes have a hole drilled in the width of a strut. A stainless steel band locks the strut's hole to a steel pipe. With this method, the struts may be cut to the exact length needed. Triangles of exterior plywood are then nailed to the struts. The dome is wrapped from the bottom to the top with several stapled layers of tar paper, in order to shed water, and finished with shingles. This type of dome is often called a hub-and-strut dome because of the use of steel hubs to tie the struts together.


==Dome homes==
Panelized domes are constructed of separately-framed timbers covered in plywood. The three members comprising the triangular frame are often cut at compound angles in order to provide for a flat fitting of the various triangles. Holes are drilled through the members at precise locations and steel bolts then connect the triangles to form the dome. These members are often 2x4's or 2x6's, which allow for more insulation to fit within the triangle. The panelized technique allows the builder to attach the plywood skin to the triangles while safely working on the ground or in a comfortable shop out of the weather. This method does not require expensive steel hubs.
Fuller hoped that the geodesic dome would help address the postwar housing crisis. This was consistent with his prior hopes for both versions of the [[Dymaxion House]].


Residential geodesic domes have been less successful than those used for working and/or entertainment, largely because of their complexity and consequent greater construction costs. Professional experienced dome contractors, while hard to find, do exist, and can eliminate much of the cost overruns associated with false starts and incorrect estimates.
Temporary greenhouse domes have been constructed by stapling plastic sheeting onto a dome constructed from one-inch square beams. The result is warm, movable by hand in sizes less than 20 feet, and cheap.
Fuller himself lived in a geodesic dome in [[Carbondale, Illinois]], at the corner of Forest Ave and Cherry St.<ref>{{cite web|url=https://maps.google.com/maps?f=q&source=s_q&hl=en&geocode=&q=Carbondale,+Illinois,Forest+and+Cherry&sll=37.727097,-89.218617&sspn=0.157225,0.304871&g=Carbondale,+Illinois,&ie=UTF8&ll=37.722885,-89.225507&spn=0.002355,0.004764&t=h&z=18&iwloc=A&layer=c&cbll=37.722766,-89.22551&panoid=AaNkKvIMPGlPFAOFvTFv6w&cbp=12,26.827702702702687,,0,-2.813555743243249 |title=Carbondale, Illinois, Forest and Cherry |publisher=Google Maps |access-date=2010-10-17}}</ref>
It should be staked to the ground to prevent it being moved by wind.
Fuller thought of residential domes as air-deliverable products manufactured by an aerospace-like industry. Fuller's own dome home still exists, the [[R. Buckminster Fuller and Anne Hewlett Dome Home]], and a group called RBF Dome NFP is attempting to restore the dome and have it registered as a [[National Historic Landmark]]. It is on the [[National Register of Historic Places listings in Jackson County, Illinois|National Register of Historic Places]].


In 1986, a patent for a dome construction technique involving [[polystyrene]] triangles laminated to reinforced concrete on the outside, and wallboard on the inside was awarded to American Ingenuity of Rockledge, Florida. The construction technique allows the domes to be prefabricated in kit form and erected by a homeowner. This method makes the seams into the strongest part of the structure, where the seams and especially the hubs in most wooden-framed domes are the weakest point in the structure. It also has the advantage of being watertight.
Steel-framework domes can be easily constructed of electrical conduit. One flattens the end of a strut and drills bolt holes at the needed length. A single bolt secures a vertex of struts. The nuts are usually set with removable locking compound, or if the dome is portable, have a castle nut with a cotter pin. This is the standard way to construct domes for jungle-gyms.


Other examples have been built in Europe. In 2012, an aluminium and glass dome was used as a dome cover to an eco home in Norway<ref>{{cite web|url=http://naturhuset.blogg.no/ |title=naturhuset - Vi skal bygge et Naturhus og en selvforsynende hage pĺ Sandhornřya i Nordland. Prosjektet er sterkt inspirert av arkitekt Bengt Warne, den russiske Bokserien The Ringing Cedars series og vĺr inderlige kjćrlighet og dype respekt for Moder Jord |publisher=Naturhuset.blogg.no |access-date=2015-08-30}}</ref> and in 2013 a glass and wood clad dome home was built in Austria.<ref>[http://www.kristallsalzwelt.com/KristallSalzWelt%20ARCHITEKTUR.html KristallSalzWelt] {{webarchive|url=https://web.archive.org/web/20160304001256/http://www.kristallsalzwelt.com/KristallSalzWelt%20ARCHITEKTUR.html |date=2016-03-04 }}</ref>
Concrete and foam plastic domes generally start with a steel framework dome, wrapped with chicken wire and wire screen for reinforcement. The chicken wire and screen is tied to the framework with wire ties. A coat of material is then sprayed or molded onto the frame. Tests should be performed with small squares to achieve the correct consistency of concrete or plastic. Generally, several coats are necessary on the inside and outside. The last step is to saturate concrete or polyester domes with a thin layer of epoxy compound to shed water.


In Chile, examples of geodesic domes are being readily adopted for hotel accommodations either as tented style geodesic domes or glass-covered domes. Examples: EcoCamp Patagonia, Chile;<ref>{{cite web|url=http://www.ecocamp.travel/Domes |title=EcoCamp Patagonia Domes » EcoCamp Patagonia |publisher=Ecocamp.travel |access-date=2015-08-30}}</ref> and Elqui Domos, Chile.<ref>[http://elquidomos.cl/site/] {{webarchive|url=https://web.archive.org/web/20130721011731/http://elquidomos.cl/site/|date=July 21, 2013}}</ref>
Some concrete domes have been constructed from prefabricated, prestressed, steel-reinforced concrete panels that can be bolted into place. The bolts are within raised receptacles covered with little concrete caps to shed water. The triangles overlap to shed water. The triangles in this method can be molded in forms patterned in sand with wooden patterns, but the concrete triangles are usually so heavy that they must be placed with a crane. This construction is well-suited to domes because there is no place for water to pool on the concrete and leak through. The metal fasteners, joints and internal steel frames remain dry, preventing frost and corrosion damage. The concrete resists sun and weathering. Some form of internal flashing or caulking must be placed over the joints to prevent drafts. The 1963 [[Cinerama Dome]] was built from [[precast concrete]] hexagons and pentagons.


=== Disadvantages ===
In 1986 a patent for a dome construction technique involving [[Polystyrene|EPS]] triangles laminated to reinforced concrete on the outside, and wallboard on the inside was awarded to American Ingenuity of Rockledge Florida. The construction technique allows the domes to be prefabricated in kit form and erected by a homeowner. This method makes the seams into the strongest part of the structure, where the seams and especially the hubs in most wooden-framed domes are the weakest point in the structure. It also has the advantage of being watertight.
[[File:Buckminster Fuller dome in Carbondale.jpg|thumb|right|[[R. Buckminster Fuller and Anne Hewlett Dome Home|Buckminster Fuller's own home]], undergoing restoration after deterioration.]]


Although dome homes enjoyed a ripple of popularity in the late 1960s and early 1970s, as a housing system, the dome has many disadvantages and problems. A former proponent of dome homes, [[Lloyd Kahn]], who wrote two books about them (''Domebook 1'' and ''Domebook 2'') and founded Shelter Publications, became disillusioned with them, calling them "smart but not wise".
==Largest geodesic dome structures==
He noted the following disadvantages, which he has listed on his company's website:
Many geodesic domes built are still in use. According to the Buckminster Fuller Institute,<ref>{{cite web|title=World's 10 Largest Domes|url=http://bfi.org/our_programs/who_is_buckminster_fuller/design_science/geodesic_domes/worlds_10_largest_domes|publisher=Buckminster Fuller Institute}}{{dead|date=June 2010}}</ref> the world's ten largest geodesic domes are{{Clarify|date=February 2010}}<!-- What do the dimensions given relate to? Height/Diameter/Radius??? The website quoted doesn't seem to say otherwise I'd add it myself. -->:
Off-the-shelf building materials (e.g., plywood, strand board) normally come in rectangular shapes, therefore some material may have to be scrapped after cutting rectangles down to triangles, increasing the cost of construction. Fire escapes are problematic; codes require them for larger structures, and they are expensive. Windows conforming to code can cost anywhere from five to fifteen times as much as windows in conventional houses. Professional electrical wiring costs more because of increased labor time. Even owner-wired situations are costly, because more of certain materials are required for dome construction. Expansion and partitioning is also difficult. Kahn notes that domes are difficult if not impossible to build with natural materials, generally requiring plastics, etc., which are polluting and deteriorate in sunlight.
* Fantasy Entertainment Complex: [[Kyosho Isle, Japan]], 710&nbsp;ft (216 m)<ref>http://www.bfi.org/our_programs/who_is_buckminster_fuller/design_science/geodesic_domes/worlds_10_largest_domes</ref>
* Multi-Purpose Arena: [[Nagoya, Japan]], 614&nbsp;ft (187 m)<ref>http://www.bfi.org/our_programs/who_is_buckminster_fuller/design_science/geodesic_domes/worlds_10_largest_domes</ref>
* [[Tacoma Dome]]: [[Tacoma, Washington]], USA, 530&nbsp;ft (161.5 m)
* [[Superior Dome]]: [[Northern Michigan University]]. [[Marquette, Michigan]], USA, 525&nbsp;ft (160 m)<ref>http://webb.nmu.edu/SportsAthletics/SiteSections/Facilities/SuperiorDome.shtml</ref>


Air stratification and moisture distribution within a dome are unusual. The conditions tend to quickly degrade wooden framing or interior paneling.
* [[Walkup Skydome]]: [[Northern Arizona University]]. [[Flagstaff, Arizona]], USA, 502&nbsp;ft (153 m) <ref>http://www.westernwoodstructures.com/</ref>
* Round Valley High School Stadium: [[Springerville]]-[[Eagar, AZ]], USA, 440&nbsp;ft (134 m)
* Former [[Spruce Goose]] Hangar: [[Long Beach, California]], USA, 415&nbsp;ft (126 m)
* Formosa Plastics Storage Facility: [[Mai Liao, Taiwan]], 402&nbsp;ft (122 m)
* Union Tank Car Maintenance Facility: [[Baton Rouge, Louisiana]], USA, 384&nbsp;ft (117) m (demolished in November 2007)<ref>http://www.2theadvocate.com/news/11880141.html</ref>
* [http://www.lehighcement.com/AboutLehigh/About_Lehigh_Union_Bridge.htm Union Lehigh Portland Cement Storage Facility]: [[Union Bridge, Maryland]], USA, 374&nbsp;ft (114 m)


Privacy is difficult to guarantee because a dome is difficult to partition satisfactorily. Sounds, smells, and even reflected light tend to be conveyed through the entire structure.
==Disadvantages of dome homes==
As a housing system, enjoying a wave of popularity in the late 1960s and early '70s, the dome can have numerous disadvantages and problems. Former proponent for, and author about, dome homes Lloyd Kahn is the founder of Shelter Publications. He has collected a lot of the criticisms and listed them on his company's Web site:


As with any curved shape, the dome produces wall areas that can be difficult to use and leaves some peripheral floor area with restricted use due to lack of headroom. Circular plan shapes lack the simple modularity provided by rectangles. Furnishers and fitters design with flat surfaces in mind. Placing a standard sofa against an exterior wall (for example) results in a crescent behind the sofa being wasted.
The shape of a dome house makes it difficult to conform to code requirements for placement of [[Plumbing drainage venting|sewer vents]] and [[chimney]]s. Off-the-shelf building materials (e.g., plywood, strand board) normally come in rectangular shapes and so much material may have to be scrapped after cutting rectangles down to triangles, thus increasing the cost of construction. Fire escapes are problematic; codes require them for larger structures, and they are expensive. Windows conforming to code can cost anywhere from 5 to 15 times as much as windows in conventional houses. Professional electrical wiring costs more because of increased labor time. Even owner-wired situations are costly, because more of certain materials are required for dome construction.


Dome builders using cut-board sheathing material (common in the 1960s and 1970s) find it hard to seal domes against rain, because of their many seams. Also, these seams may be stressed because ordinary solar heat flexes the entire structure each day as the sun moves across the sky.
Air stratification and moisture distribution within a dome are unusual, and these conditions tend to quickly degrade wooden framing or interior paneling. Privacy is difficult to guarantee because a dome is difficult to partition satisfactorily. Sounds, smells, and even reflected light tend to be conveyed through the entire structure.
Subsequent addition of straps and interior flexible drywall finishes has virtually eliminated this movement being noticed in the interior finishes.


The most effective waterproofing method with a wooden dome is to [[Roof shingle|shingle]] the dome. Peaked caps at the top of the dome, or to modify the dome shapes are used where slope is insufficient for ice barrier. One-piece reinforced [[concrete]] or [[plastic]] domes are also in use, and some domes have been constructed from plastic or waxed cardboard triangles that are overlapped in such a way as to shed water.
As with any curved shape, the dome produces wall areas that can be difficult to use and leaves some peripheral floor area with restricted use due to lack of headroom. This can leave a volume that may require heating – representing a cost in energy – but that cannot be lived in. Circular plan shapes lack the simple modularity provided by rectangles. Furnishers and fitters usually design with flat surfaces in mind, and so placing a standard sofa (for example) results in a crescent behind the sofa being wasted. This is best overcome by purpose-built fittings, though it adds to cost.


Buckminster Fuller's former student [[J. Baldwin]] insisted that no reason exists for a properly designed, well-constructed dome to leak, and that some designs 'cannot' leak.<ref>(Bucky Works: Buckminster Fuller's Ideas for Today)<!-- a page number would be welcome --></ref>
Dome builders using cut-board sheathing materials (as was common in the '60s and '70s) find it hard to seal domes against rain, because of their many seams. Also, these seams may be stressed because ordinary solar heat flexes the entire structure each day as the sun moves across the sky.


==Related patterns==
The most effective waterproofing method with a wooden dome is to [[Roof shingle|shingle]] the dome, but even this can be a problem at the top of the dome where the slope is less than that required by most roofing materials. (One solution is to add a peaked cap to the top of the dome or to modify the dome shape.) One-piece reinforced [[concrete]] or [[plastic]] domes are also in use, and some domes have been constructed from plastic or waxed cardboard triangles that are overlapped in such a way as to shed water. Buckminster Fuller's former student [[J. Baldwin]] insists that there is not any reason for a properly designed, well-constructed dome to leak, and that some designs ''cannot'' leak ''(Bucky Works: Buckminster Fuller's Ideas for Today)''.<!-- a page number would be welcome --> However, [[Lloyd Kahn]], after writing two books on the subject (''Domebook 1'' and ''Domebook 2''), became disillusioned with domes. He calls domes "smart but not wise",<ref>[http://www.shelterpub.com/_shelter/refried_domes.html "Refried Domes" by Lloyd Kahn]</ref> and has collected many of the criticisms given above.

==See also==
The building of very strong, stable structures out of patterns of reinforcing triangles<!-- WRONG!, called [[tensegrity]],--> is most commonly seen in [[tent]] design. It has been applied in the abstract in other [[industrial design]], but even in [[management science]] and deliberative [[structure]]s as a [[conceptual metaphor]], especially in the work of [[Stafford Beer]], whose "transmigration" method is based so specifically on dome design that only fixed numbers of people can take part in the process at each [[deliberation]] stage.
<div style="-moz-column-count:2; column-count:2;">

*[[Dome]]
==Largest geodesic dome structures==
*[[Concrete dome]]
{{main|List of largest domes in the world}}
*[[Cloud nine (Tensegrity sphere)]]

*[[Domed city]]
According to Guinness World Records, as of May 30, 2021,<ref name= "GWR">{{cite web|title=World's largest geodesic dome |url= https://www.guinnessworldrecords.com/world-records/632532-largest-geodesic-dome|website=www.guinnessworldrecords.com }}</ref> the [[Jeddah Super Dome]], [[Jeddah]], Saudi Arabia ({{coord|21.7496403|N|39.1516230|E}}), {{convert|210|m|abbr=on}} is the current largest geodesic dome.
*[[Fullerene]]s, molecules which resemble the geodesic dome structure

*[[Hoberman sphere]]
According to the Buckminster Fuller Institute in 2010,<ref name="bfi">{{cite web|title=World's 10 Largest Domes |url=http://bfi.org/our_programs/who_is_buckminster_fuller/design_science/geodesic_domes/worlds_10_largest_domes |publisher=Buckminster Fuller Institute |url-status=dead |archive-url=https://web.archive.org/web/20100412163621/http://www.bfi.org/our_programs/who_is_buckminster_fuller/design_science/geodesic_domes/worlds_10_largest_domes |archive-date=April 12, 2010 }}</ref> the world's 10 largest geodesic domes by diameter at that time were:
*[[Monolithic dome]]
* [[Seagaia Ocean Dome]] (シーガイアオーシャンドーム): [[Miyazaki, Miyazaki|Miyazaki]], [[Japan]] ({{coord|31.9551|N|131.4691|E}}), {{convert|216.5|m|abbr=on}}<ref name="bfi" /> — Demolished in 2017.
*[[Radome]]
* [[Nagoya Dome]] (ナゴヤドーム): [[Nagoya]], Japan ({{coord|35.1859|N|136.9474|E}}), {{convert|187.2|m|abbr=on}}<ref name="bfi"/>
*''[[Silent Running]]'' 1972 science fiction film prominently featuring geodesic domes.
* [[Superior Dome]]: [[Northern Michigan University]]. [[Marquette, Michigan]], U.S. ({{coord|46.5603|N|87.3938|W}}), {{convert|163.4|m|abbr=on}}<ref>{{cite web|url=http://webb.nmu.edu/SportsAthletics/SiteSections/Facilities/SuperiorDome.shtml |title=Superior Dome &#124; Wildcat Athletics at Northern Michigan University |publisher=Webb.nmu.edu |access-date=2010-10-17}}</ref>
*''[[Sindome]]'' An online Cyberpunk RPG that takes place in a giant geodesic dome.
* [[Tacoma Dome]]: [[Tacoma, Washington]], U.S. ({{coord|47.2367|N|122.4270|W}}), {{convert|161.5|m|abbr=on}}
*[[Space frame]]s
* [[Walkup Skydome]]: [[Northern Arizona University]]. [[Flagstaff, Arizona]], U.S. ({{coord|35.1805|N|111.6529|W}}), {{convert|153|m|abbr=on}}<ref>{{cite web|author=WWSI |url=http://www.westernwoodstructures.com/ |title=Western Wood Structures, Inc. - Glulam Beams, Arches and Bridges |publisher=Westernwoodstructures.com |access-date=2010-10-17}}</ref>
*[[Stepan Center]]
* [[Round Valley Ensphere]]: [[Springerville]]-[[Eagar, AZ]], U.S. ({{coord|34.1204|N|109.2849|W}}), {{convert|134|m|abbr=on}}
*[[Thin-shell structure|Shell structure]]
* Former [[Spruce Goose]] Hangar: [[Long Beach, California]], U.S. ({{coord|33.7513|N|118.1889|W}}), {{convert|126|m|abbr=on}} — later owned by [[Carnival Cruise Line]], and [[Google]].
*[[Gridshell]]
* [[Formosa Plastics Corp|Formosa Plastics]] Storage Facility: [[Mailiao]], Taiwan ({{coord|23.8007|N|120.1947|E}}), {{convert|122|m|abbr=on}} — Eleven domes.
*[[Truss]]
* [[Union Tank Car Company|Union Tank Car]] Maintenance Facility: [[Baton Rouge, Louisiana]], U.S. ({{coord|30.5827|N|91.2344|W}}), {{convert|117|m|abbr=on}} — Demolished in 2007.
*[[Synergetics (Fuller)|Synergetics]]
* [[HeidelbergCement|Lehigh]] Portland Cement Storage Facility: [[Union Bridge, Maryland]], U.S. ({{coord|39.5590|N|77.1718|W}}), {{convert|114|m|abbr=on}}
*[[Tent#Flexible_poles|Geodesic tents]]

*[[Pentakis dodecahedron]]
The Fuller Institute list is now dated. Several important domes missed or built later are now in the top 10. Currently, many geodesic domes are larger than {{Convert|113|m|ft}} in diameter.<ref name="Domes of over 100m">{{cite web|url=https://www.geometrica.com/en/latestnews/over-100 |title=Domes of over 100m |date=12 November 2018 |publisher=geometrica.com |access-date=2019-05-04}}</ref>
*[[Truncated icosahedron]]

</div>
* [[Poliedro de Caracas]] ("Caracas Polyhedron Arena"), [[Caracas]], Venezuela ({{coord|10.4338|N|66.9385|W}}), {{convert|143|m|abbr=on}}<ref>{{cite web|url=https://www.britannica.com/technology/building-construction/High-rise-construction-since-1945#ref105247/ |title=Postwar developments in long-span construction |publisher=britannica.com |access-date=2017-06-07}}</ref>
* [[San Cristóbal mine (Bolivia)|San Cristóbal mine]] (MSC) Dome, [[Colcha "K" Municipality]], Bolivia ({{coord|21.1246|S|67.2096|W}}), {{convert|140|m|abbr=on}}<ref>{{cite web|url=http://geometrica.com/en/San-cristobal-news/ |title=The Largest Storage Dome in South America |publisher=geometrica.com |access-date=2017-06-07}}</ref>
* [[Ruwais Refinery]] Dome, [[Ruwais]], United Arab Emirates ({{coord|24.1459|N|52.7392|E}}), {{convert|135|m|abbr=on}}<ref name="Domes of over 100m"/>

== See also ==
* {{annotated link|Geodesic grid}}
* {{annotated link|Fly's Eye Dome}}
* {{annotated link|Hoberman sphere}}


==References==
==References==
{{Reflist|colwidth=30em}}
{{Refimprove|date=August 2007}}
{{Reflist}}


==External links==
==External links==
{{sister project links|d=Q1135180|b=Geodesic Grids|c=category:Geodesic domes|wikt=geodesic dome|n=no|v=no|voy=no|m=no|mw=no|species=no|s=no|q=no}}
{{External links|date=January 2010}}
{{Wiktionary}}
{{Commons category|Geodesic domes}}
* [http://domemountain.spaces.live.com Dome being constructed: 45x37 ft., on WV mountain, detailed pictures, forums and external links to other Geodesic Dome sites]
* [http://www.cjfearnley.com/fuller-faq-4.html The R. Buckminster Fuller FAQ: Geodesic Domes]
* [http://www.cjfearnley.com/fuller-faq-4.html The R. Buckminster Fuller FAQ: Geodesic Domes]
* [http://simplydifferently.org/Geodesic_Dome_Notes Geodesic Dome Notes]: 57 dome variants featured (1V to 10V) of various solids (icosa, cube, octa, etc)
* [http://simplydifferently.org/Geodesic_Dome_Notes Geodesic Dome Notes]: 57 dome variants featured (1V to 10V) of various solids (icosa, cube, octa, etc.)
* [http://www.mero-tsk.de/uploads/tx_cwtcartoongallery/Eden_Project_english.pdf Article about the Eden Domes (PDF file 5.1 MB)]
* [https://web.archive.org/web/20130514052843/http://www.mero-tsk.de/uploads/tx_cwtcartoongallery/Eden_Project_english.pdf Article about the Eden Domes] (PDF file 5.1 MB)
* [http://www.merouk.co.uk/structures/2000eden.htm Construction of the Eden Project Biomes]
* [http://www.3doro.de/kuppel.htm Geodaetische Kuppeln (Geodesic Domes)] by T. E. Dorozinski
* [http://www.3doro.de/kuppel.htm Geodaetische Kuppeln (Geodesic Dome) by T.E. Dorozinski]
* [http://www.dome-scape.com/english/fa_02.htm A meta-geodesic dome – made of quads instead of triangles] by F. Tuczek
* [https://www.desertdomes.com Desert Domes], resources about creating domes
* [http://geometrydome.com Geometry Dome]: geodesic dome design without corner connectors, featured in the Guggenheim Museum and at [http://www.burningman.com BurningMan]
* [http://lib.engg.nagoya-u.ac.jp/doc/kiyou/pdf/50_1L.pdf Shape optimization of Shell and Spatial structure]
* [http://sketchup.google.com/3dwarehouse/cldetails?mid=1f33552966b6f22224e5217d8a2e013a&num=50&scoring=a 3D Warehouse - Geodesic Collection] Catalog(s) of free 3D digital models for [http://sketchup.google.com/index.html ''Google SketchUp''] and [http://earth.google.com/index.html ''Google Earth'']


[[Category:Buckminster Fuller]]
{{Buckminster Fuller}}
[[Category:House types]]
[[Category:Geodesic domes| ]]
[[Category:Domes| Geodesic dome]]


{{Mathematical art}}
[[da:Geodætisk kuppel]]

[[de:Geodätische Kuppel]]
[[Category:Geodesic domes| ]]
[[es:Cúpula geodésica]]
[[Category:1960s fads and trends]]
[[fr:Géode]]
[[Category:Buckminster Fuller]]
[[it:Cupola geodetica]]
[[Category:Architecture related to utopias]]
[[he:כיפה גאודזית]]
[[nl:Geodetische koepel]]
[[ja:ジオデシック・ドーム]]
[[pl:Kopuła geodezyjna]]
[[pt:Cúpula geodésica]]
[[ro:Dom geodezic]]
[[ru:Геодезический купол]]
[[simple:Geodesic dome]]
[[sk:Geodetická kopula]]
[[sv:Geodetisk kupol]]
[[ta:கோளப்பரப்புக் குவிமாடம்]]

Latest revision as of 13:49, 6 November 2024

The Montreal Biosphère, formerly the American Pavilion of Expo 67, by R. Buckminster Fuller, on Île Sainte-Hélène, Montreal, Quebec

A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The rigid triangular elements of the dome distribute stress throughout the structure, making geodesic domes able to withstand very heavy loads for their size.

History

[edit]
Spaceship Earth at Epcot
The Climatron greenhouse at Missouri Botanical Gardens, built in 1960 and designed by Thomas C. Howard of Synergetics, Inc., inspired the domes in the science fiction movie Silent Running.
Science World in Vancouver
Science World in Vancouver, built for Expo 86, and inspired by Buckminster Fuller's Geodesic dome.
RISE, public art designed by Wolfgang Buttress, located in Belfast, consists of two spheres which utilise Buckminster Fuller's Geodesic dome.

The first geodesic dome was designed after World War I by Walther Bauersfeld,[1] chief engineer of Carl Zeiss Jena, an optical company, for a planetarium to house his planetarium projector. An initial, small dome was patented and constructed by the firm of Dykerhoff and Wydmann on the roof of the Carl Zeiss Werke in Jena, Germany. A larger dome, called "The Wonder of Jena", opened to the public in July 1926.[2]

Twenty years later, Buckminster Fuller coined the term "geodesic" from field experiments with artist Kenneth Snelson at Black Mountain College in 1948 and 1949. Although Fuller was not the original inventor, he is credited with the U.S. popularization of the idea for which he received U.S. patent 2682235A on 29 June 1954.[3] The oldest surviving dome built by Fuller himself is located in Woods Hole, Massachusetts, and was built by students under his tutelage over three weeks in 1953.[4]

The geodesic dome appealed to Fuller because it was extremely strong for its weight, its "omnitriangulated" surface provided an inherently stable structure, and because a sphere encloses the greatest volume for the least surface area.

The dome was successfully adopted for specialized uses, such as the 21 Distant Early Warning Line domes built in Canada in 1956,[5] the 1958 Union Tank Car Company dome near Baton Rouge, Louisiana, designed by Thomas C. Howard of Synergetics, Inc. and specialty buildings such as the Kaiser Aluminum domes (constructed in numerous locations across the US, e.g., Virginia Beach, Virginia), auditoriums, weather observatories, and storage facilities. The dome was soon breaking records for covered surface, enclosed volume, and construction speed.

Beginning in 1954, the U.S. Marines experimented with helicopter-deliverable geodesic domes. A 30-foot wood and plastic geodesic dome was lifted and carried by helicopter at 50 knots without damage, leading to the manufacture of a standard magnesium dome by Magnesium Products of Milwaukee. Tests included assembly practices in which previously untrained Marines were able to assemble a 30-foot magnesium dome in 135 minutes, helicopter lifts off aircraft carriers, and a durability test in which an anchored dome successfully withstood without damage, a day-long 120 mph (190 km/h) propeller blast from the twin 3,000 horsepower engines of an anchored airplane.[6]

The 1958 Gold Dome in Oklahoma City, Oklahoma, utilized Fuller's design for use as a bank building. Another early example was the Stepan Center at the University of Notre Dame, built in 1962.[7]

The dome was introduced to a wider audience as a pavilion for the 1964 New York World's Fair designed by Thomas C. Howard of Synergetics, Inc. This dome is now used as an aviary by the Queens Zoo in Flushing Meadows Corona Park.[8]

Another dome is from Expo 67 at the Montreal World's Fair, where it was part of the American Pavilion. The structure's covering later burned, but the structure itself still stands and, under the name Biosphère, currently houses an interpretive museum about the Saint Lawrence River.

In the 1970s, Zomeworks licensed plans for structures based on other geometric solids, such as the Johnson solids, Archimedean solids, and Catalan solids.[9] These structures may have some faces that are not triangular, being squares or other polygons.

In 1975, a dome was constructed at the South Pole, where its resistance to snow and wind loads was important.

On October 1, 1982, one of the most famous geodesic domes, Spaceship Earth at Epcot in Walt Disney World Resort in Bay Lake, Florida, just outside of Orlando opened. The building and the ride inside of it are named with one of Buckminster Fuller's famous terms, Spaceship Earth, a world view expressing concern over the use of limited resources available on Earth and encouraging everyone on it to act as a harmonious crew working toward the greater good. The building is Epcot's icon, representing the entire park.

For the 1986 World's Fair (Expo 86), held in Vancouver, a Buckminster Fuller-inspired Geodesic dome was designed by the Expo's chief architect Bruno Freschi to serve as the fair's Expo Centre. Construction began in 1984 and was completed by early 1985. The dome and the building now serve as an Arts, Science and Technology center, and has been named Science World.[10]

In 2000, the world's first fully sustainable geodesic dome hotel, EcoCamp Patagonia, was built at Kawésqar National Park in Chilean Patagonia,[11] opening the following year in 2001. The hotel's dome design is key to resisting the region's strong winds and is based on the dwellings of the indigenous Kaweskar people. Geodomes are also becoming popular as a glamping (glamorous camping) unit.

Methods of construction

[edit]
Long Island Green Dome

Wooden domes have a hole drilled in the width of a strut. A stainless steel band locks the strut's hole to a steel pipe. With this method, the struts may be cut to the exact length needed. Triangles of exterior plywood are then nailed to the struts. The dome is wrapped from the bottom to the top with several stapled layers of tar paper, to shed water, and finished with shingles. This type of dome is often called a hub-and-strut dome because of the use of steel hubs to tie the struts together.

Paneled domes are constructed of separately framed timbers covered in plywood. The three members comprising the triangular frame are often cut at compound angles to provide for a flat fitting of the various triangles. Holes are drilled through the members at precise locations and steel bolts then connect the triangles to form the dome. These members are often 2x4s or 2x6s, which allow for more insulation to fit within the triangle. The panelized technique allows the builder to attach the plywood skin to the triangles while safely working on the ground or in a comfortable shop out of the weather. This method does not require expensive steel hubs.

Steel framework can be easily constructed of electrical conduit. One flattens the end of a strut and drills bolt holes at the needed length. A single bolt secures a vertex of struts. The nuts are usually set with removable locking compound, or if the dome is portable, have a castellated nut with a cotter pin. This is the standard way to construct domes for jungle gyms.

Domes can also be constructed with a lightweight aluminium framework which can either be bolted or welded together or can be connected with a more flexible nodal point/hub connection. These domes are usually clad with glass which is held in place with a PVC coping, which can be sealed with silicone to make it watertight. Some designs allow for double glazing or for insulated panels to be fixed in the framework.

Concrete and foam-plastic domes generally start with a steel framework dome, wrapped with chicken wire and wire screen for reinforcement. The chicken wire and screen are tied to the framework with wire ties. A coat of material is then sprayed or molded onto the frame. Tests should be performed with small squares to achieve the correct consistency of concrete or plastic. Generally, several coats are necessary on the inside and outside. The last step is to saturate concrete or polyester domes with a thin layer of epoxy compound to shed water.

Some concrete domes have been constructed from prefabricated, prestressed, steel-reinforced concrete panels that can be bolted into place. The bolts are within raised receptacles covered with little concrete caps to shed water. The triangles overlap to shed water. The triangles in this method can be molded in forms patterned in sand with wooden patterns, but the concrete triangles are usually so heavy that they must be placed with a crane. This construction is well-suited to domes because no place allows water to pool on the concrete and leak through. The metal fasteners, joints, and internal steel frames remain dry, preventing frost and corrosion damage. The concrete resists sun and weathering. Some form of internal flashing or caulking must be placed over the joints to prevent drafts. The 1963 Cinerama Dome was built from precast concrete hexagons and pentagons.

Domes can now be printed at high speeds using very large, mobile "3D Printers", also known as additive manufacturing machines. The material used as the filament is often a form of air injected concrete or closed-cell plastic foam.

Given the complicated geometry of the geodesic dome, dome builders rely on tables of strut lengths, or "chord factors". In Geodesic Math and How to Use It, Hugh Kenner wrote, "Tables of chord factors, containing as they do the essential design information for spherical systems, were for many years guarded like military secrets. As late as 1966, some 3ν icosa figures from Popular Science Monthly were all anyone outside the circle of Fuller licensees had to go on." (page 57, 1976 edition). Other tables became available with publication of Lloyd Kahn's Domebook 1 (1970) and Domebook 2 (1971).

Dome homes

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Fuller hoped that the geodesic dome would help address the postwar housing crisis. This was consistent with his prior hopes for both versions of the Dymaxion House.

Residential geodesic domes have been less successful than those used for working and/or entertainment, largely because of their complexity and consequent greater construction costs. Professional experienced dome contractors, while hard to find, do exist, and can eliminate much of the cost overruns associated with false starts and incorrect estimates. Fuller himself lived in a geodesic dome in Carbondale, Illinois, at the corner of Forest Ave and Cherry St.[12] Fuller thought of residential domes as air-deliverable products manufactured by an aerospace-like industry. Fuller's own dome home still exists, the R. Buckminster Fuller and Anne Hewlett Dome Home, and a group called RBF Dome NFP is attempting to restore the dome and have it registered as a National Historic Landmark. It is on the National Register of Historic Places.

In 1986, a patent for a dome construction technique involving polystyrene triangles laminated to reinforced concrete on the outside, and wallboard on the inside was awarded to American Ingenuity of Rockledge, Florida. The construction technique allows the domes to be prefabricated in kit form and erected by a homeowner. This method makes the seams into the strongest part of the structure, where the seams and especially the hubs in most wooden-framed domes are the weakest point in the structure. It also has the advantage of being watertight.

Other examples have been built in Europe. In 2012, an aluminium and glass dome was used as a dome cover to an eco home in Norway[13] and in 2013 a glass and wood clad dome home was built in Austria.[14]

In Chile, examples of geodesic domes are being readily adopted for hotel accommodations either as tented style geodesic domes or glass-covered domes. Examples: EcoCamp Patagonia, Chile;[15] and Elqui Domos, Chile.[16]

Disadvantages

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Buckminster Fuller's own home, undergoing restoration after deterioration.

Although dome homes enjoyed a ripple of popularity in the late 1960s and early 1970s, as a housing system, the dome has many disadvantages and problems. A former proponent of dome homes, Lloyd Kahn, who wrote two books about them (Domebook 1 and Domebook 2) and founded Shelter Publications, became disillusioned with them, calling them "smart but not wise". He noted the following disadvantages, which he has listed on his company's website: Off-the-shelf building materials (e.g., plywood, strand board) normally come in rectangular shapes, therefore some material may have to be scrapped after cutting rectangles down to triangles, increasing the cost of construction. Fire escapes are problematic; codes require them for larger structures, and they are expensive. Windows conforming to code can cost anywhere from five to fifteen times as much as windows in conventional houses. Professional electrical wiring costs more because of increased labor time. Even owner-wired situations are costly, because more of certain materials are required for dome construction. Expansion and partitioning is also difficult. Kahn notes that domes are difficult if not impossible to build with natural materials, generally requiring plastics, etc., which are polluting and deteriorate in sunlight.

Air stratification and moisture distribution within a dome are unusual. The conditions tend to quickly degrade wooden framing or interior paneling.

Privacy is difficult to guarantee because a dome is difficult to partition satisfactorily. Sounds, smells, and even reflected light tend to be conveyed through the entire structure.

As with any curved shape, the dome produces wall areas that can be difficult to use and leaves some peripheral floor area with restricted use due to lack of headroom. Circular plan shapes lack the simple modularity provided by rectangles. Furnishers and fitters design with flat surfaces in mind. Placing a standard sofa against an exterior wall (for example) results in a crescent behind the sofa being wasted.

Dome builders using cut-board sheathing material (common in the 1960s and 1970s) find it hard to seal domes against rain, because of their many seams. Also, these seams may be stressed because ordinary solar heat flexes the entire structure each day as the sun moves across the sky. Subsequent addition of straps and interior flexible drywall finishes has virtually eliminated this movement being noticed in the interior finishes.

The most effective waterproofing method with a wooden dome is to shingle the dome. Peaked caps at the top of the dome, or to modify the dome shapes are used where slope is insufficient for ice barrier. One-piece reinforced concrete or plastic domes are also in use, and some domes have been constructed from plastic or waxed cardboard triangles that are overlapped in such a way as to shed water.

Buckminster Fuller's former student J. Baldwin insisted that no reason exists for a properly designed, well-constructed dome to leak, and that some designs 'cannot' leak.[17]

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The building of very strong, stable structures out of patterns of reinforcing triangles is most commonly seen in tent design. It has been applied in the abstract in other industrial design, but even in management science and deliberative structures as a conceptual metaphor, especially in the work of Stafford Beer, whose "transmigration" method is based so specifically on dome design that only fixed numbers of people can take part in the process at each deliberation stage.

Largest geodesic dome structures

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According to Guinness World Records, as of May 30, 2021,[18] the Jeddah Super Dome, Jeddah, Saudi Arabia (21°44′59″N 39°09′06″E / 21.7496403°N 39.1516230°E / 21.7496403; 39.1516230), 210 m (690 ft) is the current largest geodesic dome.

According to the Buckminster Fuller Institute in 2010,[19] the world's 10 largest geodesic domes by diameter at that time were:

The Fuller Institute list is now dated. Several important domes missed or built later are now in the top 10. Currently, many geodesic domes are larger than 113 metres (371 ft) in diameter.[22]

See also

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References

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  1. ^ First Geodesic Dome: Planetarium in Jena 1922 incl. patent information Archived March 19, 2013, at the Wayback Machine
  2. ^ "Zeiss-Planetarium Jena: Geschichte". Planetarium-jena.de. Archived from the original on 2015-08-31. Retrieved 2015-08-30.
  3. ^ For a more detailed historical account, see the chapter "Geodesics, Domes, and Spacetime" in Tony Rothman's book Science à la Mode, Princeton University Press, 1989.
  4. ^ "The Woods Hole Dome". Archived from the original on 2 July 2019. Retrieved 2019-07-02.
  5. ^ "Audio interview with Bernard Kirschenbaum on DEW Line domes". Bernardkirschenbaum.com. Archived from the original on 2011-04-20. Retrieved 2010-10-17.
  6. ^ Fuller, R. Buckminster; Marks, Robert (1973). The Dymaxion World of Buckminster Fuller. Anchor Books. p. 203. ISBN 0-385-01804-5.
  7. ^ Archives, Notre Dame (17 September 2010). "Mid-Century Modern". Notre Dame Archives News & Notes. Retrieved 15 July 2019.
  8. ^ Gray, Christopher (1993-01-03). "Streetscapes: The Queens Aviary; A Great Outside Interior Space". The New York Times. ISSN 0362-4331. Retrieved 2024-06-01.
  9. ^ Geodesic domes are most often based on Platonic solids, particularly the icosahedron.
  10. ^ Science World – OMNIMAX Theatre – OMNIMAX Facts Archived 2006-06-26 at the Wayback Machine
  11. ^ "EcoCamp, the world's first geodesic dome hotel". domerama.com. Archived from the original on 15 February 2013. Retrieved 2 February 2022.
  12. ^ "Carbondale, Illinois, Forest and Cherry". Google Maps. Retrieved 2010-10-17.
  13. ^ "naturhuset - Vi skal bygge et Naturhus og en selvforsynende hage pĺ Sandhornřya i Nordland. Prosjektet er sterkt inspirert av arkitekt Bengt Warne, den russiske Bokserien The Ringing Cedars series og vĺr inderlige kjćrlighet og dype respekt for Moder Jord". Naturhuset.blogg.no. Retrieved 2015-08-30.
  14. ^ KristallSalzWelt Archived 2016-03-04 at the Wayback Machine
  15. ^ "EcoCamp Patagonia Domes » EcoCamp Patagonia". Ecocamp.travel. Retrieved 2015-08-30.
  16. ^ [1] Archived July 21, 2013, at the Wayback Machine
  17. ^ (Bucky Works: Buckminster Fuller's Ideas for Today)
  18. ^ "World's largest geodesic dome". www.guinnessworldrecords.com.
  19. ^ a b c "World's 10 Largest Domes". Buckminster Fuller Institute. Archived from the original on April 12, 2010.
  20. ^ "Superior Dome | Wildcat Athletics at Northern Michigan University". Webb.nmu.edu. Retrieved 2010-10-17.
  21. ^ WWSI. "Western Wood Structures, Inc. - Glulam Beams, Arches and Bridges". Westernwoodstructures.com. Retrieved 2010-10-17.
  22. ^ a b "Domes of over 100m". geometrica.com. 12 November 2018. Retrieved 2019-05-04.
  23. ^ "Postwar developments in long-span construction". britannica.com. Retrieved 2017-06-07.
  24. ^ "The Largest Storage Dome in South America". geometrica.com. Retrieved 2017-06-07.
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