# Great cubicuboctahedral prism

Great cubicuboctahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGoccope
Coxeter diagramx x4/3x3o4*b ()
Elements
Cells8 triangular prisms, 6 cubes, 6 octagrammic prisms, 2 great cubicuboctahedra
Faces16 triangles, 12+24+24 squares, 12 octagrams
Edges24+48+48
Vertices48
Vertex figureIsosceles trapezoidal pyramid, edge lengths 1, 2–2, 2, 2–2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{3-\sqrt2}{2}} ≈ 0.89045}$
Hypervolume${\displaystyle 2\frac{4\sqrt2-3}{3} ≈ 1.77124}$
Dichoral anglesTrip–4–stop: ${\displaystyle \arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439^\circ}$
Gocco–4–cube: 90°
Gocco–3–trip: 90°
Gocco–8/3–stop: 90°
Cube–4–stop: 90°
Height1
Central density4
Number of pieces64
Related polytopes
ArmySemi-uniform Ticcup
RegimentGoccope
DualGreat hexacronic icositetrahedral tegum
ConjugateSmall cubicuboctahedral prism
Abstract properties
Euler characteristic–6
Topological properties
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame
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.

## Vertex coordinates

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

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