Great truncated cuboctahedron

Great truncated cuboctahedron
Type Uniform star polyhedron
Elements F = 26, E = 72
V = 48 (χ = 2)
Faces by sides 12{4}+8{6}+6{8/3}
Coxeter diagram
Wythoff symbol 2 3 4/3 |
Symmetry group Oh, [4,3], *432
Index references U20, C67, W93
Dual polyhedron Great disdyakis dodecahedron
Vertex figure
4.6/5.8/3
Bowers acronym Quitco

In geometry, the great truncated cuboctahedron (or quasitruncated cuboctahedron or stellatruncated cuboctahedron) is a nonconvex uniform polyhedron, indexed as U20. It has 26 faces (12 squares, 8 hexagons and 6 octagrams), 72 edges, and 48 vertices.[1] It is represented by the Schläfli symbol tr{4/3,3}, and Coxeter-Dynkin diagram . It is sometimes called the quasitruncated cuboctahedron because it is related to the truncated cuboctahedron, , except that the octagonal faces are replaced by {8/3} octagrams.

3D model of a great truncated cuboctahedron

Convex hull

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Its convex hull is a nonuniform truncated cuboctahedron. The truncated cuboctahedron and the great truncated cuboctahedron form isomorphic graphs despite their different geometric structure.

 
Convex hull
 
Great truncated cuboctahedron

Orthographic projections

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Cartesian coordinates

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Cartesian coordinates for the vertices of a great truncated cuboctahedron centered at the origin are all permutations of  

See also

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References

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  1. ^ Maeder, Roman. "20: great truncated cuboctahedron". MathConsult. Archived from the original on 2020-02-17.
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