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

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

External links

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