|Bowers style acronym||Cope|
|Coxeter diagram||x o4x3o ()|
|Cells||8 triangular prisms, 6 cubes, 2 cuboctahedra|
|Faces||16 triangles, 12+24 squares|
|Vertex figure||Rectangular pyramid, edge lengths 1, √ (base), √ (legs)|
|Measures (edge length 1)|
|Number of external pieces||16|
|Level of complexity||8|
|Dual||Rhombic dodecahedral tegum|
|Abstract & topological properties|
|Symmetry||B3×A1, order 96|
The cuboctahedral prism or cope is a prismatic uniform polychoron that consists of 2 cuboctahedra, 6 cubes and 8 triangular prisms. Each vertex joins 1 cuboctahedron, 2 cubes, and 2 triangular prisms. As the name suggests, it is a prism based on the cuboctahedron. As such it is also a convex segmentochoron (designated K-4.43 on Richard Klitzing's list).
Gallery[edit | edit source]
Vertex coordinates[edit | edit source]
The vertices of a cuboctahedral prism of edge length 1 are given by all permutations and sign changes of the first three coordinates of:
Representations[edit | edit source]
A cuboctahedral prism has the following Coxeter diagrams:
- x o4x3o (full symmetry)
- x x3o3x () (rhombitetratetrahedral prism)
- s2s4x3o () (bases as rhombitetratetrahedra)
- oo4xx3oo&#x (bases considered separately)
- xx3oo3xx&#x (rhombitetratetrahedral bases considered separately)
- xxx xox4oqo&#xt (BC2×A1 axial, cube-first)
- xxx xxo3oxx&#xt (A2×A1 axial, triangular prism-first)
- xxx qqo qoq oqq&#zx (A1×A1×A1×A1 symmetry)
Related polychora[edit | edit source]
A cuboctahedral prism can be cut in half to produce two triangular cupolic prisms with the base triangular prisms in rotated orientations.
[edit | edit source]
- Bowers, Jonathan. "Category 19: Prisms" (#908).
- Klitzing, Richard. "Cope".
- Wikipedia Contributors. "Cuboctahedral prism".