Small icosihemidodecahedron: Difference between revisions
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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).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 U<sub>49</sub>. Its [[vertex figure]] alternates two regular triangles and [[decagon]]s as a [[antiparallelogram|crossed quadrilateral]]. |
In [[geometry]], the '''small icosihemidodecahedron''' (or '''small icosahemidodecahedron''') is a [[uniform star polyhedron]], indexed as U<sub>49</sub>. It has 26 faces (20 [[Triangle|triangles]] and 6 [[Decagon|decagons]]), 60 edges, and 30 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|url-status=live|archive-url=|archive-date=|access-date=}}</ref> Its [[vertex figure]] alternates two regular triangles and [[decagon]]s as a [[antiparallelogram|crossed quadrilateral]]. |
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It is given a [[Wythoff symbol]], '''3 |
It is given a [[Wythoff symbol]], '''{{frac|3|2}} 3 | 5''', but that construction represents a double covering of this model. |
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It is a [[hemipolyhedron]] with its six decagonal faces passing through the model center. |
It is a [[hemipolyhedron]] with its six decagonal faces passing through the model center. |
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* [[Pentakis icosidodecahedron]] |
* [[Pentakis icosidodecahedron]] |
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* [[List of uniform polyhedra]] |
* [[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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Revision as of 21:19, 16 March 2020
| 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 given a Wythoff symbol, 3⁄2 3 | 5, but that construction represents a double covering of this model.
It is a hemipolyhedron with its six decagonal faces passing through the model center.
Related polyhedra
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
References
- ^ Maeder, Roman. "49: small icosihemidodecahedron". MathConsult.
{{cite web}}: CS1 maint: url-status (link)
External links
 | This polyhedron-related article is a stub. You can help Wikipedia by expanding it. |