Great truncated cuboctahedron

Great truncated cuboctahedron
File:Great truncated cuboctahedron.png
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	Template:CDD
Wythoff symbol
Symmetry group	Oh, [4,3], *432
Index references	U20, C67, W93
Dual polyhedron	Great disdyakis dodecahedron
Vertex figure	File:Great truncated cuboctahedron vertfig.png 4.6/5.8/3
Bowers acronym	Quitco

File:Great truncated cuboctahedron.stl

3D model of a 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. It is represented by the Schläfli symbol tr{⁴/₃,3}, and Coxeter-Dynkin diagram Template:CDD. It is sometimes called the quasitruncated cuboctahedron because it is related to the truncated cuboctahedron, Template:CDD, 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.

File:Great truncated cuboctahedron convex hull.png Convex hull

File:Great truncated cuboctahedron.png Great truncated cuboctahedron

Orthographic projections

File:Great truncated cuboctahedron ortho wireframes.png

Cartesian coordinates

Cartesian coordinates for the vertices of a great truncated cuboctahedron with side length 2 centered at the origin are all permutations of $$(\pm 1,\pm [1-\sqrt{2}],\pm [1-2\sqrt{2}]).$$

See also

• List of uniform polyhedra

External links

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