Hemidodecahedron (4-dimensional)
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| Hemidodecahedron (4-dimensional) | |
|---|---|
| Rank | 3 |
| Dimension | 4 |
| Type | Regular |
| Notation | |
| Schläfli symbol | [note 1] |
| Elements | |
| Faces | 6 pentagonal-pentagrammic coils |
| Edges | 15 |
| Vertices | 10 |
| Vertex figure | Triangle |
| Petrie polygons | 6 pentagonal-pentagrammic coils |
| Related polytopes | |
| Army | Rap |
| Petrie dual | Hemidodecahedron (4-dimensional) |
| Convex hull | Rectified pentachoron |
| Abstract & topological properties | |
| Flag count | 60 |
| Euler characteristic | 1 |
| Schläfli type | {5,3} |
| Orientable | No |
| Genus | 1 |
| Skeleton | Petersen graph |
| Properties | |
| Symmetry | A4+, order 60 |
| Chiral | Yes |
| Convex | No |
| Dimension vector | (2,2,2) |
The 4-dimensional realization of the hemidodecahedron is a regular skew polyhedron in 4-dimensional space. It is one of two pure realizations of the hemidodecahedron, and the lowest dimensional realization of the hemidodecahedron overall.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of the rectified pentachoron.[1]
External links[edit | edit source]
- Hartley, Michael. "{5,3}*60".
- Wikipedia contributors. "Hemi-dodecahedron".
Notes[edit | edit source]
- ↑ This symbol is ambiguous, as it is shared by another realization of the hemidodecahedron in 5-dimensional space.
References[edit | edit source]
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. Cambridge University Press. ISBN 0-521-81496-0.
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