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, so the pentagonal pyramids requires tall isosceles triangle faces.
The dual to the dodecahedral pyramid is an icosahedral pyramid, seen as an icosahedral base, and 12 regular tetrahedral meeting at an apex.