Great truncated cuboctahedron

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.

Great truncated cuboctahedron
TypeUniform star polyhedron
ElementsF = 26, E = 72
V = 48 (χ = 2)
Faces by sides12{4}+8{6}+6{8/3}
Wythoff symbol2 3 4/3 |
Symmetry groupOh, [4,3], *432
Index referencesU20, C67, W93
Dual polyhedronGreat disdyakis dodecahedron
Vertex figure
4.6/5.8/3
Bowers acronymQuitco
3D model of a great truncated cuboctahedron

Convex hull

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

Cartesian coordinates

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

(±1, ±(1−√2), ±(1−2√2)).
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References
  1. Maeder, Roman. "20: great truncated cuboctahedron". MathConsult.

See also
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