Great cubicuboctahedral prism

Great cubicuboctahedral prism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Goccope
Coxeter diagram	x x4/3x3o4*b ()
Elements
Cells	8 triangular prisms, 6 cubes, 6 octagrammic prisms, 2 great cubicuboctahedra
Faces	16 triangles, 12+24+24 squares, 12 octagrams
Edges	24+48+48
Vertices	48
Vertex figure	Isosceles trapezoidal pyramid, edge lengths 1, √2–√2, √2, √2–√2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{3-\sqrt2}{2}} ≈ 0.89045$
Hypervolume	$2\frac{4\sqrt2-3}{3} ≈ 1.77124$
Dichoral angles	Trip–4–stop: $\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439^\circ$
	Gocco–4–cube: 90°
	Gocco–3–trip: 90°
	Gocco–8/3–stop: 90°
	Cube–4–stop: 90°
Height	1
Central density	4
Number of pieces	64
Related polytopes
Army	Semi-uniform Ticcup
Regiment	Goccope
Dual	Great hexacronic icositetrahedral tegum
Conjugate	Small cubicuboctahedral prism
Abstract properties
Euler characteristic	–6
Topological properties
Orientable	Yes
Properties
Symmetry	B3×A1, order 96
Convex	No
Nature	Tame
Discovered by	{{{discoverer}}}

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

The great cubicuboctahedral prism can be vertex-inscribed into the great tesseractitesseractihexadecachoron.

Cross-sections

Vertex coordinates

The vertices of a great cubicuboctahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

• $\left(±\frac{\sqrt2-1}{2},\,±\frac12,\,±\frac12,\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#932).

• Klitzing, Richard. "goccope".