Dodecahedral pyramid
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's circumradius is greater than its edge length,[1] the pentagonal pyramids require tall isosceles triangle faces.
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 |
The dual to the dodecahedral pyramid is an icosahedral pyramid, seen as an icosahedral base, and 12 regular tetrahedra 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
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.