Great cubicuboctahedron

Great cubicuboctahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gocco
Coxeter diagram	x4/3x3o4*a ()
Elements
Faces	8 triangles, 6 squares, 6 octagrams
Edges	24+24
Vertices	24
Vertex figure	Isosceles trapezoid, edge lengths 1, √2–√2, √2, √2–√2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{5-2\sqrt2}}{2} \approx 0.73681$
Volume	$2\frac{4\sqrt2-3}{3} \approx 1.77124$
Dihedral angles	8/3–3: $\arccos\left(-\frac{\sqrt3}{3}\right) \approx 125.26439^\circ$
	8/3–4: 90°
Central density	4
Number of external pieces	62
Level of complexity	13
Related polytopes
Army	Tic
Regiment	Gocco
Dual	Great hexacronic icositetrahedron
Conjugate	Small cubicuboctahedron
Convex core	Cube
Abstract & topological properties
Flag count	192
Euler characteristic	-4
Orientable	Yes
Genus	3
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

The great cubicuboctahedron, or gocco, is a uniform polyhedron. It consists of 8 triangles, 6 squares, and 6 octagrams. One triangle, one square, and two octagrams meet at each vertex. It also has 12 square pseudofaces.

Vertex coordinates

A small rhombicuboctahedron of edge length 1 has vertex coordinates given by all permutations of:

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

Related polyhedra

The great cubicuboctahedron is the colonel of a three-member regiment that also includes the quasirhombicuboctahedron and the great rhombihexahedron.

The rhombiquasihyperhombicosicosahedron is a uniform polyhedron compound composed of 5 great cubicuboctahedra.

o4/3o3o4*a truncations

Name	OBSA	CD diagram	Picture
(degenerate, double cover of cube)		x4/3o3o4*a ()
Great cubicuboctahedron	gocco	x4/3x3o4*a ()
(degenerate, oct+6(4))		o4/3x3o4*a ()
(degenerate, double cover of cho)		o4/3x3x4*a ()
(degenerate, oct+6(4))		o4/3o3x4*a ()
Small cubicuboctahedron	socco	x4/3o3x4*a ()
Cuboctatruncated cuboctahedron	cotco	x4/3x3x4*a ()

External links

• Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#45).

• Klitzing, Richard. "gocco".

• Wikipedia Contributors. "Great cubicuboctahedron".
• McCooey, David. "Great Cubicuboctahedron"