Great rhombicuboctahedral prism
Great rhombicuboctahedral prism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Gircope 
Coxeter diagram  x x4x3x () 
Elements  
Cells  12 cubes, 8 hexagonal prisms, 6 octagonal prisms, 2 great rhombicuboctahedra 
Faces  24+24+24+24 squares, 16 hexagons, 12 octagons 
Edges  48+48+48+48 
Vertices  96 
Vertex figure  Irregular tetrahedron, edge lengths √2, √3, √2+√2 (base), √2 (legs) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Cube–4–hip: 
Cube–4–op: 135°  
Hip–4–op:  
Girco–8–op: 90°  
Girco–6–hip: 90°  
Girco–4–cube: 90°  
Height  1 
Central density  1 
Number of external pieces  28 
Level of complexity  24 
Related polytopes  
Army  Gircope 
Regiment  Gircope 
Dual  Disdyakis dodecahedral tegum 
Conjugate  Quasitruncated cuboctahedral prism 
Abstract & topological properties  
Flag count  2304 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  B_{3}×A_{1}, order 96 
Convex  Yes 
Nature  Tame 
The great rhombicuboctahedral prism (OBSA: gircope) is a prismatic uniform polychoron that consists of 2 great rhombicuboctahedra, 6 octagonal prisms, 8 hexagonal prisms, and 12 cubes. Each vertex joins one of each type of cell. As the name suggests, it is a prism based on the great rhombicuboctahedron. As such it is also a convex segmentochoron (designated K4.125 on Richard Klitzing's list).
The great rhombicuboctahedral prism can be obtained as the central segment of the prismatorhombated tesseract in rhombicuboctahedronfirst orientation.
This polychoron can be alternated into a snub cubic antiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a pyritosnub alterprism, which is also nonuniform.
Gallery[edit  edit source]

Net
Vertex coordinates[edit  edit source]
The vertices of a great rhombicuboctahedral prism of edge length 1 are given by all permutations of the first three coordinates of:
 .
Representations[edit  edit source]
The great rhombicuboctahedral prism has the following Coxeter diagrams:
 x x4x3x () (full symmetry)
 xx4xx3xx&#x (bases considered separately)
 xxxxxx xuxxux4xxwwxx&#xt (BC_{2}×A_{1} symmetry, octagonal prismfirst)
External links[edit  edit source]
 Bowers, Jonathan. "Category 19: Prisms" (#944).
 Klitzing, Richard. "Gircope".
 Wikipedia contributors. "Truncated cuboctahedral prism".