Small cubicuboctahedral prism

Small cubicuboctahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Soccope
Coxeter diagram	x x4/3o3x4*b ()
Elements
Cells	8 triangular prisms, 6 cubes, 6 octagonal prisms, 2 small cubicuboctahedra
Faces	16 triangles, 12+24+24 squares, 12 octagons
Edges	24+48+48
Vertices	48
Vertex figure	Crossed isosceles trapezoidal pyramid, edge lengths 1, √2+√2, √2, √2+√2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3+\sqrt2}{2}} ≈ 1.48563$
Hypervolume	$2\frac{3+4\sqrt2}{3} ≈ 5.77214$
Dichoral angles	Socco–4–cube: 90°
	Socco–3–trip: 90°
	Socco–8–op: 90°
	Cube–4–op: 90°
	Trip–4–op: $\arccos\left(\frac{\sqrt3}{3}\right) ≈ 54.73561^\circ$
Height	1
Central density	2
Number of pieces	80
Related polytopes
Army	Sircope
Regiment	Sircope
Dual	Small hexacronic icositetrahedral tegum
Conjugate	Great cubicuboctahedral prism
Abstract properties
Euler characteristic	–6
Topological properties
Orientable	Yes
Properties
Symmetry	B3×A1, order 96
Convex	No
Nature	Tame

The small cubicuboctahedral prism or soccope is a prismatic uniform polychoron that consists of 2 small cubicuboctahedra, 6 cubes, 8 triangular prisms, and 6 octagonal prisms. Each vertex joins 1 small cubicuboctahedron, 1 triangular prism, 1 cube, and 2 octagonal prisms. As the name suggests, it is a prism based on the small cubicuboctahedron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small rhombicuboctahedral prism.

External links

• Bowers, Jonathan. "Category 19: Prisms" (#924).

• Klitzing, Richard. "soccope".