Cubitruncated cuboctahedron

Cubitruncated cuboctahedron
Cubitruncated cuboctahedron.png
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 Cubitruncated cuboctahedron vertfig.png
Bowers acronym Cotco

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]

3D model of a cubitruncated cuboctahedron

Convex hullEdit

Its convex hull is a nonuniform truncated cuboctahedron.

Convex hull
Cubitruncated cuboctahedron

Orthogonal projectionEdit


Cartesian coordinatesEdit

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

(±(2−1), ±1, ±(2+1))

Related polyhedraEdit

Tetradyakis hexahedronEdit

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


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 alsoEdit


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

External linksEdit