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.
 | This article relies largely or entirely on a single source. (April 2024) |
| Dodecahedral pyramid | ||
|---|---|---|
 Schlegel diagram | ||
| Type | Polyhedral pyramid | |
| Schläfli symbol | ( ) ∨ {5,3} | |
| Cells | 13 | 1 {5,3}  12 ( ) ∨ {5}  |
| Faces | 42 | 30 ()v{ } 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 20 regular tetrahedra meeting at an apex.
