Great cubicuboctahedron

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

In geometry, the great cubicuboctahedron is a nonconvex uniform polyhedron, indexed as U14.

Orthographic projections[edit]

Great cubicuboctahedron ortho wireframes.png

Related polyhedra[edit]

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 hexahedron.png
Truncated cube
Uniform great rhombicuboctahedron.png
Nonconvex great rhombicuboctahedron
Great cubicuboctahedron.png
Great cubicuboctahedron
Great rhombihexahedron.png
Great rhombihexahedron

Great hexacronic icositetrahedron[edit]

Great hexacronic icositetrahedron
DU14 great hexacronic icositetrahedron.png
Type Star polyhedron
Face DU14 facets.png
Elements F = 24, E = 48
V = 20 (χ = −4)
Symmetry group Oh, [4,3], *432
Index references DU14
dual polyhedron Great cubicuboctahedron

The great hexacronic icositetrahedron is the dual of the great cubicuboctahedron.

See also[edit]


  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, doi:10.1017/CBO9780511569371, ISBN 978-0-521-54325-5, MR 0730208

External links[edit]