Hemidodecahedron
Jump to navigation
Jump to search
| Hemidodecahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular |
| Notation | |
| Bowers style acronym | Eldoe |
| Schläfli symbol | [1][2] [2] |
| Elements | |
| Faces | 6 pentagons |
| Edges | 15 |
| Vertices | 10 |
| Vertex figure | Triangle |
| Petrie polygons | 6 pentagons |
| Related polytopes | |
| Dual | Hemiicosahedron |
| Petrie dual | Hemidodecahedron[2] |
| Orientation double cover | Dodecahedron |
| Abstract & topological properties | |
| Flag count | 60 |
| Euler characteristic | 1 |
| Schläfli type | {5,3} |
| Surface | Real projective plane[1] |
| Orientable | No |
| Genus | 1 |
| Skeleton | Peterson graph |
| Properties | |
| Symmetry | A5, order 60 |
The hemidodecahedron is a regular map and abstract polytope. It is a tiling of the projective plane. It can be seen as an dodecahedron with antipodal faces identified.
Realizations[edit | edit source]
The hemidodecahedron has two pure realizations. One in 4-dimensions and one in 5-dimensions.[3]
External links[edit | edit source]
- Hartley, Michael. "{5,3}*60".
- Wikipedia Contributors. "Hemi-dodecahedron".
- Klitzing, Richard. Abstract polytopes
References[edit | edit source]
- ↑ 1.0 1.1 McMullen & Schulte (2002:163)
- ↑ 2.0 2.1 2.2 McMullen & Schulte (1997:455)
- ↑ McMullen & Schulte (2002:138)
Bibliography[edit | edit source]
- McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF). Discrete Computational Geometry (47): 449–478. doi:10.1007/PL00009304.
- McMullen, Peter; Schulte, Egon (December 2002), Abstract Regular Polytopes (1st ed.), Cambridge University Press, ISBN 0-521-81496-0
 | This article is a stub. You can help Polytope Wiki by expanding it. |