Cubitruncated cuboctahedron

In geometry, the cubitruncated cuboctahedron or cuboctatruncated cuboctahedron is a nonconvex uniform polyhedron, indexed as U16. It has 20 faces (8 hexagons, 6 octagons, and 6 octagrams), 72 edges, and 48 vertices.[1]

Cubitruncated cuboctahedron
TypeUniform star polyhedron
ElementsF = 20, E = 72
V = 48 (χ = 4)
Faces by sides8{6}+6{8}+6{8/3}
Wythoff symbol
Symmetry groupOh, [4,3], *432
Index referencesU16, C52, W79
Dual polyhedronTetradyakis hexahedron
Vertex figure
6.8.8/3
Bowers acronymCotco
3D model of a cubitruncated cuboctahedron

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))

Tetradyakis hexahedron

Tetradyakis hexahedron
TypeStar polyhedron
Face
ElementsF = 48, E = 72
V = 20 (χ = 4)
Symmetry groupOh, [4,3], *432
Index referencesDU16
dual polyhedronCubitruncated cuboctahedron
3D model of a tetradyakis hexahedron

The tetradyakis hexahedron (or great disdyakis dodecahedron) is a nonconvex isohedral polyhedron. It has 48 intersecting scalene triangle faces, 72 edges, and 20 vertices.

Proportions

The triangles have one angle of , one of and one of . The dihedral angle equals . Part of each triangle lies within the solid, hence is invisible in solid models.

It is the dual of the uniform cubitruncated cuboctahedron.

See also

References

  1. Maeder, Roman. "16: cubitruncated cuboctahedron". MathConsult.


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