Nonconvex great rhombicuboctahedron

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Nonconvex great rhombicuboctahedron
Uniform great rhombicuboctahedron.png
Type Uniform star polyhedron
Elements F = 26, E = 48
V = 24 (χ = 2)
Faces by sides 8{3}+(6+12){4}
Wythoff symbol 3/2 4 | 2
3 4/3 | 2
Symmetry group Oh, [4,3], *432
Index references U17, C59, W85
Dual polyhedron Great deltoidal icositetrahedron
Vertex figure Uniform great rhombicuboctahedron vertfig.png
4.4.4.3/2
Bowers acronym Querco

In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U17. It is represented by Schläfli symbol t0,2{4,3/2} and Coxeter-Dynkin diagram of CDel node 1.pngCDel 4.pngCDel node.pngCDel d3.pngCDel rat.pngCDel d2.pngCDel node 1.png. Its vertex figure is a crossed quadrilateral.

This model shares the name with the convex great rhombicuboctahedron, also called the truncated cuboctahedron.

An alternate name for this figure is quasirhombicuboctahedron. From that derives its Bowers acronym: querco.

Orthogonal projections[edit]

Nonconvex great rhombicuboctahedron ortho wireframes.png

Related polyhedra[edit]

It shares the vertex arrangement with the convex truncated cube. It additionally shares its edge arrangement with the great cubicuboctahedron (having the triangular faces and 6 square faces in common), and with the great rhombihexahedron (having 12 square faces in common). It has the same vertex figure as the pseudo great rhombicuboctahedron, which is not a uniform polyhedron.

Truncated hexahedron.png
Truncated cube
Uniform great rhombicuboctahedron.png
Great rhombicuboctahedron
Great cubicuboctahedron.png
Great cubicuboctahedron
Great rhombihexahedron.png
Great rhombihexahedron
Pseudo-great rhombicuboctahedron.png
pseudo great rhombicuboctahedron

Great deltoidal icositetrahedron[edit]

Great deltoidal icositetrahedron
DU17 great strombic icositetrahedron.png
Type Star polyhedron
Face DU17 facets.png
Elements F = 24, E = 48
V = 26 (χ = 2)
Symmetry group Oh, [4,3], *432
Index references DU17
dual polyhedron Nonconvex great rhombicuboctahedron

The great deltoidal icositetrahedron is the dual of the nonconvex great rhombicuboctahedron.

References[edit]

External links[edit]

Weisstein, Eric Wolfgang. "Great Deltoidal Icositetrahedron". MathWorld.