Icosahedral pyramid

The icosahedral pyramid is a four-dimensional convex polytope, bounded by one icosahedron as its base and by 20 triangular pyramid cells which meet at its apex. Since an icosahedron's circumradius is less than its edge length,[1] the tetrahedral pyramids can be made with regular faces.

Icosahedral pyramid

Schlegel diagram
Type Polyhedral pyramid
Schläfli symbol ( ) ∨ {3,5}
Cells 21 1 {3,5}
20 ( ) ∨ {3}
Faces 50 20+30 {3}
Edges 12+30
Vertices 13
Dual Dodecahedral pyramid
Symmetry group H3, [5,3,1], order 120
Properties convex, regular-faces

The regular 600-cell has icosahedral pyramids around every vertex.

The dual to the icosahedral pyramid is the dodecahedral pyramid, seen as a dodecahedral base, and 12 regular pentagonal pyramids meeting at an apex.

References

  1. Klitzing, Richard. "3D convex uniform polyhedra x3o5o - ike"., circumradius sqrt[(5+sqrt(5))/8 = 0.951057


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