Great cubicuboctahedron

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]

Great cubicuboctahedron
TypeUniform star polyhedron
ElementsF = 20, E = 48
V = 24 (χ = −4)
Faces by sides8{3}+6{4}+6{8/3}
Coxeter diagram
Wythoff symbol3 4 | 4/3
4 3/2 | 4
Symmetry groupOh, [4,3], *432
Index referencesU14, C50, W77
Dual polyhedronGreat hexacronic icositetrahedron
Vertex figure
3.8/3.4.8/3
Bowers acronymGocco
3D model of a great cubicuboctahedron

Orthographic projections

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
TypeStar polyhedron
Face
ElementsF = 24, E = 48
V = 20 (χ = −4)
Symmetry groupOh, [4,3], *432
Index referencesDU14
dual polyhedronGreat cubicuboctahedron
3D model of a great hexacronic icositetrahedron

The great hexacronic icositetrahedron (or great lanceal disdodecahedron) is the dual of the great cubicuboctahedron.

See also

References
  1. Maeder, Roman. "14: great cubicuboctahedron". MathConsult.
  2. Webb, Robert. "Great Cubicuboctahedron". Stella: Polyhedron Navigator.


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