Cuboctahedral pyramid | ||
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![]() 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.