Nonconvex great rhombicuboctahedron

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File:Nonconvex great rhombicuboctahedron.stl

3D model of a nonconvex great rhombicuboctahedron

In geometry, the nonconvex great rhombicuboctahedron is a nonconvex uniform polyhedron, indexed as U₁₇. It has 26 faces (8 triangles and 18 squares), 48 edges, and 24 vertices.^[1] It is represented by the Schläfli symbol rr{4,Template:Frac} and Coxeter-Dynkin diagram of Template:CDD. Its vertex figure is a crossed quadrilateral.

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

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

Orthographic projections

Error creating thumbnail:

Cartesian coordinates

Cartesian coordinates for the vertices of a nonconvex great rhombicuboctahedron centered at the origin with edge length 1 are all the permutations of

$(\pm [\sqrt{2} - 1], \pm 1, \pm 1) .$

Related polyhedra

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.

File:Truncated hexahedron.png Truncated cube	File:Uniform great rhombicuboctahedron.png Great rhombicuboctahedron	File:Great cubicuboctahedron.png Great cubicuboctahedron	File:Great rhombihexahedron.png Great rhombihexahedron	Error creating thumbnail: Pseudo great rhombicuboctahedron