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Nonconvex great rhombicuboctahedron
Nonconvex uniform polyhedron with 26 faces / From Wikipedia, the free encyclopedia
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{4,3⁄2} and Coxeter-Dynkin diagram of . Its vertex figure is a crossed quadrilateral.
Nonconvex great rhombicuboctahedron | |
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Type | Uniform star polyhedron |
Elements | F = 26, E = 48 V = 24 (χ = 2) |
Faces by sides | 8{3}+(6+12){4} |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 | ![]() 4.4.4.3/2 |
Bowers acronym | Querco |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Nonconvex_great_rhombicuboctahedron.stl/640px-Nonconvex_great_rhombicuboctahedron.stl.png)
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.