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}
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) is a nonconvex uniform polyhedron, indexed as U₂₀. It is represented by 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.

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)).

See also

• List of uniform polyhedra

External links

• Weisstein, Eric W., "Great truncated cuboctahedron", MathWorld.