Dodecahedral pyramid
Dodecahedral pyramid | ||
---|---|---|
Schlegel diagram | ||
Type | Polyhedral pyramid | |
Schläfli symbol | ( ) ∨ {5,3} | |
Cells | 13 | 1 {5,3} 12 ( ) ∨ {5} |
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 requires tall isosceles triangle 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
- ↑ Klitzing, Richard. "3D convex uniform polyhedra o3o5x - doe". sqrt[(9+3 sqrt(5))/8] = 1.401259
External links
- Olshevsky, George. "Pyramid". Glossary for Hyperspace. Archived from the original on 4 February 2007.
- Richard Klitzing, Axial-Symmetrical Edge Facetings of Uniform Polyhedra
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