Small rhombicuboctahedral prism
Small rhombicuboctahedral prism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Sircope 
Coxeter diagram  x x4o3x () 
Elements  
Cells  8 triangular prisms, 6+12 cubes, 2 small rhombicuboctahedra 
Faces  16 triangles, 12+24+24+24 squares 
Edges  24+48+48 
Vertices  48 
Vertex figure  Isosceles trapezoidal pyramid, edge lengths 1, √2, √2, √2 (base), √2 (legs) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Trip–4–cube: 
Cube–4–cube: 135°  
Sirco–4–cube: 90°  
Sirco–3–trip: 90°  
Height  1 
Central density  1 
Number of external pieces  28 
Level of complexity  16 
Related polytopes  
Army  Sircope 
Regiment  Sircope 
Dual  Deltoidal icositetrahedral tegum 
Conjugate  Quasirhombicuboctahedral prism 
Abstract & topological properties  
Flag count  1536 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  B_{3}×A_{1}, order 96 
Convex  Yes 
Nature  Tame 
The small rhombicuboctahedral prism or sircope is a prismatic uniform polychoron that consists of 2 small rhombicuboctahedra, 6+12 cubes, and 8 triangular prisms. Each vertex joins 1 small rhombicuboctahedron, 1 triangular prism, and 3 cubes. As the name suggests, it is a prism based on the small rhombicuboctahedron. As such it is also a convex segmentochoron (designated K4.66 on Richard Klitzing's list).
The small rhombicuboctahedral prism can be obtained from the small disprismatotesseractihexadecachoron by removing 2 cube atop small rhombicuboctahedron segmentochora.
Gallery[edit  edit source]

Card with cell counts, verf, and crosssections

Segmentochoron display, sirco atop sirco

Net
Vertex coordinates[edit  edit source]
The vertices of a small rhombicuboctahedral prism of edge length 1 are given by all permutations of the first three coordinates of:
Representations[edit  edit source]
A small rhombicuboctahedral prism has the following Coxeter diagrams:
 x x4o3x (full symmetry)
 x2x4s3s () (bases as snubs)
 xx4oo3xx&#x (bases considered separately)
 xxxx xxxx4oxxo&#xt (BC_{2}×A_{1} symmetry, cubefirst)
 xxx wxx xwx xxw&#zx (A_{1}×A_{1}×A_{1}×A_{1} symmetry)
Related polychora[edit  edit source]
The small rhombicuboctahedral prism can be constructed by attaching squarre cupolic prisms to 2 opposite octagonal prisms of the squareoctagonal duoprism.
The regiment of the small rhombicuboctahedral prism also includes the small cubicuboctahedral prism and the small rhombihexahedral prism.
External links[edit  edit source]
 Bowers, Jonathan. "category 19: Prisms" (#923).
 Klitzing, Richard. "Sircope".
 Wikipedia contributors. "Rhombicuboctahedral prism".