Cubitruncated cuboctahedron

Cubitruncated cuboctahedron
Type	Uniform star polyhedron
Elements	F = 20, E = 72 V = 48 (χ = −4)
Faces by sides	8{6}+6{8}+6{^8/3}
Wythoff symbol	3 4 ^4/3 |
Symmetry group	Oh, [4,3], *432
Index references	U16, C52, W79
Dual polyhedron	Tetradyakis hexahedron
Vertex figure	6.8.^8/3
Bowers acronym	Cotco

In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U₁₆.

Convex hull

Its convex hull is a nonuniform truncated cuboctahedron.

Convex hull

Cubitruncated cuboctahedron

Orthogonal projection

Cartesian coordinates

Cartesian coordinates for the vertices of a cubitruncated cuboctahedron are all the permutations of

(±(√2−1), ±1, ±(√2+1))

Related polyhedra

Tetradyakis hexahedron

Tetradyakis hexahedron
Type	Star polyhedron
Face
Elements	F = 48, E = 72 V = 20 (χ = −4)
Symmetry group	Oh, [4,3], *432
Index references	DU16
dual polyhedron	Cubitruncated cuboctahedron

The tetradyakis hexahedron is a nonconvex isohedral polyhedron. It has 48 intersecting scalene triangle faces, 72 edges, and 20 vertices.

It is the dual of the uniform cubitruncated cuboctahedron.

See also

• List of uniform polyhedra

References

• Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 730208 p. 92

External links

• Weisstein, Eric W., "Cubitruncated cuboctahedron", MathWorld.
• Weisstein, Eric W., "Tetradyakis hexahedron", MathWorld.
• http://gratrix.net Uniform polyhedra and duals