Petrial great stellated dodecahedron
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| Petrial great stellated dodecahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular |
| Space | Spherical |
| Notation | |
| Schläfli symbol | [1] |
| Elements | |
| Faces | 6 skew decagons |
| Edges | 30 |
| Vertices | 20 |
| Vertex figure | Triangle |
| Related polytopes | |
| Regiment | Gissid |
| Petrie dual | Great stellated dodecahedron |
| Conjugate | Petrial dodecahedron |
| Convex hull | Dodecahedron |
| Abstract & topological properties | |
| Flag count | 120 |
| Euler characteristic | -4 |
| Schläfli type | {10,3} |
| Orientable | No |
| Genus | 6 |
| Properties | |
| Convex | No |
The petrial great stellated dodecahedron is a regular skew polyhedron and is the Petrie dual of the great stellated dodecahedron, and so it shares both of its vertices and edges with the great stellated dodecahedron. It consists of 6 skew decagrams and has an Euler characteristic of -4.
Vertex coordinates
The vertices of the petrial great stellated dodecahedron are identical to those of the great stellated dodecahedron, which is the regiment colonel.
Related polyhedra
The rectification of the petrial great stellated dodecahedron is the great icosihemidodecahedron, which is uniform.
External links
- Wikipedia Contributors. "Petrie dual".
References
Bibliography
- McMullen, Peter; Schulte, Egon (1997). "Regular Polytopes in Ordinary Space" (PDF). Discrete Computational Geometry (47): 449–478. doi:10.1007/PL00009304.