Great cubicuboctahedron

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
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), 18 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 great suffix serves to distinguish it from the small cubicuboctahedron, which also has faces in the aforementioned directions.[2]

3D model of a great cubicuboctahedron

Orthographic projectionsEdit

 

Related polyhedraEdit

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 icositetrahedronEdit

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

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

See alsoEdit

ReferencesEdit

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

External linksEdit