Great cubicuboctahedron

Great cubicuboctahedron

Type	Uniform star polyhedron
Elements	F = 20, E = 48 V = 24 (χ = −4)
Faces by sides	8{3}+6{4}+6{8/3}
Coxeter diagram
Wythoff symbol	3 4 \| 4/3 4 3/2 \| 4
Symmetry group	O_h, [4,3], *432
Index references	U₁₄, C₅₀, W₇₇
Dual polyhedron	Great hexacronic icositetrahedron
Vertex figure	3.8/3.4.8/3
Bowers acronym	Gocco

In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U₁₄. It has 20 faces (8 triangles, 6 squares and 6 octagrams), 48 edges, and 24 vertices.^[1] Its square faces and its octagrammic faces are parallel to those of a cube, while its triangular faces are parallel to those of an octahedron: hence the name cubicuboctahedron. The prefix great serves to distinguish it from the small cubicuboctahedron, which also has faces in the aforementioned directions.^[2]

Orthographic projections

Related polyhedra

It shares the vertex arrangement with the convex truncated cube and two other nonconvex uniform polyhedra. It additionally shares its edge arrangement with the nonconvex great rhombicuboctahedron (having the triangular faces and 6 square faces in common), and with the great rhombihexahedron (having the octagrammic faces in common).

Truncated cube	Nonconvex great rhombicuboctahedron	Great cubicuboctahedron	Great rhombihexahedron

Great hexacronic icositetrahedron

Great hexacronic icositetrahedron

Type	Star polyhedron
Face
Elements	F = 24, E = 48 V = 20 (χ = −4)
Symmetry group	O_h, [4,3], *432
Index references	DU₁₄
dual polyhedron	Great cubicuboctahedron