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 ()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.

References

  1. Klitzing, Richard. "3D convex uniform polyhedra o3o5x - doe". sqrt[(9+3 sqrt(5))/8] ≒ 1.401259
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