Cuboctahedral prism
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 K4.43 on Richard Klitzing's list).
Cuboctahedral prism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Cope 
Coxeter diagram  x o4x3o () 
Elements  
Cells  8 triangular prisms, 6 cubes, 2 cuboctahedra 
Faces  16 triangles, 12+24 squares 
Edges  12+48 
Vertices  24 
Vertex figure  Rectangular pyramid, edge lengths 1, √2 (base), √2 (legs) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Cube–4–trip: 
Co–4–cube: 90°  
co–3–trip: 90°  
Height  1 
Central density  1 
Number of external pieces  16 
Level of complexity  8 
Related polytopes  
Army  Cope 
Regiment  Cope 
Dual  Rhombic dodecahedral tegum 
Conjugate  None 
Abstract & topological properties  
Flag count  768 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  B_{3}×A_{1}, order 96 
Flag orbits  8 
Convex  Yes 
Nature  Tame 
Gallery edit

Net
Vertex coordinates edit
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
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 (BC_{2}×A_{1} axial, cubefirst)
 xxx xxo3oxx&#xt (A_{2}×A_{1} axial, triangular prismfirst)
 xxx qqo qoq oqq&#zx (A_{1}×A_{1}×A_{1}×A_{1} symmetry)
Related polychora edit
A cuboctahedral prism can be cut in half to produce two triangular cupolic prisms with the base triangular prisms in rotated orientations.
The regiment of the cuboctahedral prism also includes the octahemioctahedral prism and the cubohemioctahedral prism.
External links edit
 Bowers, Jonathan. "Category 19: Prisms" (#908).
 Klitzing, Richard. "Cope".
 Wikipedia contributors. "Cuboctahedral prism".