Small icosihemidodecahedron: Difference between revisions
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[[File:Small icosihemidodecahedron.stl|thumb|3D model of a small icosihemidodecahedron]] |
[[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 |
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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It is given a [[Wythoff symbol]], {{math|{{frac|3|2}} 3 {{!}} 5,}} but that construction represents a double covering of this model. |
It is given a [[Wythoff symbol]], {{math|{{frac|3|2}} 3 {{!}} 5,}} but that construction represents a double covering of this model. |
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 | ![]() ![]() ![]() ![]() |
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 |
![](/upwiki/wikipedia/commons/thumb/6/6e/Small_icosihemidodecahedron.stl/220px-Small_icosihemidodecahedron.stl.png)
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]