Small icosihemidodecahedron: Difference between revisions
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{{short description|Uniform star polyhedron with 26 faces}} |
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{{Uniform polyhedra db|Uniform polyhedron stat table|lIhD}} |
{{Uniform polyhedra db|Uniform polyhedron stat table|lIhD}} |
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[[File:Small icosihemidodecahedron.stl|thumb|3D model of a small icosihemidodecahedron]] |
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In [[geometry]], the '''small icosihemidodecahedron''' (or '''small icosahemidodecahedron''') is a [[uniform star polyhedron]], indexed as {{math|U{{sub|49}}}}. It has 26 faces (20 [[Triangle|triangles]] and 6 [[Decagon|decagons]]), 60 [[Edge (geometry)|edges]], and 30 [[Vertex (geometry)|vertices]].<ref>{{Cite web|url=https://www.mathconsult.ch/enwiki/static/unipoly/49.html|title=49: small icosihemidodecahedron|last=Maeder|first=Roman|date=|website=MathConsult|archive-url=|archive-date=|access-date=}}</ref> Its [[vertex figure]] alternates two regular triangles and [[decagon]]s as a [[antiparallelogram|crossed quadrilateral]]. It is a [[hemipolyhedron]] with its six decagonal faces passing through the model center. |
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Its 30 vertices and 60 edges, along with its 20 triangular faces, are shared with the [[icosidodecahedron]]. |
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It is given a [[Wythoff symbol]], {{math|{{frac|3|2}} 3 {{!}} 5,}} but that construction represents a double covering of this model. |
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== Related polyhedra == |
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It shares its [[edge arrangement]] with the [[icosidodecahedron]] (its [[convex hull]], having the triangular faces in common), and with the [[small dodecahemidodecahedron]] (having the decagonal faces in common). |
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{| class="wikitable" width="400" style="vertical-align:top;text-align:center" |
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|align=center|[[Image:Icosidodecahedron.png|100px]]<BR>[[Icosidodecahedron]] |
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|align=center|[[Image:Small icosihemidodecahedron.png|100px]]<BR>'''Small icosihemidodecahedron''' |
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|align=center|[[Image:Small dodecahemidodecahedron.png|100px]]<BR>[[Small dodecahemidodecahedron]] |
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|} |
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== See also == |
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* [[Pentakis icosidodecahedron]] |
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* [[List of uniform polyhedra]] |
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== References == |
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{{Reflist}} |
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== External links == |
== External links == |
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* {{mathworld | urlname = SmallIcosihemidodecahedron| title = Small icosihemidodecahedron}} |
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* [[VRML]] model: [http://www.physics.orst.edu/~bulatov/polyhedra/uniform/u54.html] |
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* [http://gratrix.net/polyhedra/uniform/summary Uniform polyhedra and duals] |
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{{Nonconvex polyhedron navigator}} |
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[[Category:Polyhedra]] |
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[[ja:小二十面半十二面体]] |
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Latest revision as of 11:28, 27 September 2023
| Small icosihemidodecahedron | |
|---|---|
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| Type | Uniform star polyhedron |
| Elements | F = 26, E = 60 V = 30 (χ = −4) |
| Faces by sides | 20{3}+6{10} |
| Coxeter diagram |     (double covering)
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| Wythoff symbol | 3/2 3 | 5 (double covering) |
| Symmetry group | Ih, [5,3], *532 |
| Index references | U49, C63, W89 |
| Dual polyhedron | Small icosihemidodecacron |
| Vertex figure |  3.10.3/2.10 |
| Bowers acronym | Seihid |
In geometry, the small icosihemidodecahedron (or small icosahemidodecahedron) is a uniform star polyhedron, indexed as U49. It has 26 faces (20 triangles and 6 decagons), 60 edges, and 30 vertices.[1] Its vertex figure alternates two regular triangles and decagons as a crossed quadrilateral. It is a hemipolyhedron with its six decagonal faces passing through the model center.
It is given a Wythoff symbol, 3⁄2 3 | 5, but that construction represents a double covering of this model.
Related polyhedra
[edit]It shares its edge arrangement with the icosidodecahedron (its convex hull, having the triangular faces in common), and with the small dodecahemidodecahedron (having the decagonal faces in common).
 Icosidodecahedron |
Small icosihemidodecahedron |
 Small dodecahemidodecahedron |
See also
[edit]References
[edit]- ^ Maeder, Roman. "49: small icosihemidodecahedron". MathConsult.
External links
[edit]
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