Small icosihemidodecahedron: Difference between revisions
m (GR) File renamed: File:Small Icosihemidodecahedron (STL).stl → File:Small icosihemidodecahedron.stl Criterion 1 (original uploader’s request) · It's unnecessary to specify the file extension. |
m short description Tags: Mobile edit Mobile app edit iOS app edit |
||
| Line 1: | Line 1: | ||
{{short description|Uniform star polyhedron with 26 faces}} |
|||
{{Uniform polyhedra db|Uniform polyhedron stat table|lIhD}} |
{{Uniform polyhedra db|Uniform polyhedron stat table|lIhD}} |
||
[[File:Small icosihemidodecahedron.stl|thumb|3D model of a small icosihemidodecahedron]] |
[[File:Small icosihemidodecahedron.stl|thumb|3D model of a small icosihemidodecahedron]] |
||
| ⚫ | In [[geometry]], the '''small icosihemidodecahedron''' (or '''small icosahemidodecahedron''') is a [[uniform star polyhedron]], indexed as U |
||
| ⚫ | 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|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]]. 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. |
|||
== Related polyhedra == |
== Related polyhedra == |
||
Revision as of 08:58, 1 June 2022
| Small icosihemidodecahedron | |
|---|---|
| |
| Type | Uniform star polyhedron |
| Elements | F = 26, E = 60 V = 30 (χ = −4) |
| Faces by sides | 20{3}+6{10} |
| Coxeter diagram |     (double covering)
|
| 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
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. |