Cuboctahedral pyramid
# Cuboctahedral pyramid

Cuboctahedral pyramid :

| Schlegel diagram |||
| - | - | - |
| Type | Polyhedral pyramid | Polyhedral pyramid |
| Schläfli symbol | ( ) ∨ r{4,3} | ( ) ∨ r{4,3} |
| Cells | 15 | 1 cuboctahedron 6 square pyramids 8 triangular pyramids |
| Faces | 38: | 8+24 triangles 6 squares |
| Edges | 36 | 36 |
| Vertices | 13 | 13 |
| Dual | rhombic dodecahedral pyramid | rhombic dodecahedral pyramid |
| Symmetry group | $B_3,$ [4,3,1], order 48 | $B_3,$ [4,3,1], order 48 |
| Properties | convex | 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, 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.

