Dodecahedral pyramid
| Dodecahedral pyramid | ||
|---|---|---|
 Schlegel diagram | ||
| Type | Polyhedral pyramid | |
| Schläfli symbol | ( ) ∨ {5,3} | |
| Cells | 13 | 1 dodecahedron  12 pentagonal pyramids  |
| Faces | 42 | 30 {3} 12 {5} |
| Edges | 50 | |
| Vertices | 21 | |
| Dual | icosahedral pyramid | |
| Symmetry group | H3, [5,3,1], order 120 | |
| Properties | convex | |
In 4-dimensional geometry, the dodecahedral pyramid is bounded by one dodecahedron on the base and 12 pentagonal pyramid cells which meet at the apex. Since a dodecahedron has a circumradius divided by edge length greater than one,[1] so the pentagonal pyramids can not made with regular faces.
The dual to the dodecahedral pyramid is a icosahedral pyramid, seen as an icosahedral base, and 12 regular tetrahedral meeting at an apex.
References
- ↑ Richard Klitzing, 3D convex uniform polyhedra, o3o5x - doe sqrt[(9+3 sqrt(5))/8] = 1.401259
External links
- Olshevsky, George, Pyramid at Glossary for Hyperspace.
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Wikimedia Commons has media related to Pyramids (geometry). |
- Richard Klitzing, Axial-Symmetrical Edge Facetings of Uniform Polyhedra