Cuboctahedral pyramid

Schlegel diagram
Type Polyhedral pyramid
Schläfli symbol ( ) ∨ r{4,3}
Cells 15 1 cuboctahedron
6 square pyramids
8 triangular pyramids
Faces 38: 8+24 triangles
6 squares
Edges 36
Vertices 13
Dual rhombic dodecahedral pyramid
Symmetry group B3, [4,3,1], order 48
Properties convex

In 4-dimensional geometry, the cuboctahedral pyramid is bounded by one cuboctahedron on the base, 6 square pyramid, and 8 triangular pyramid cells which meet at the apex. It has 38 faces: 32 triangles and 6 squares. It has 32 edges, and 13 vertices.

Since a cuboctahedron's circumradius is equal to its edge length,[1] the triangles must be taller than equilateral to create a positive height.

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

References

  1. Klitzing, Richard. "3D convex uniform polyhedra o3x4o - co".


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