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A cuboctahedron is a uniform three-dimensional polyhedron that can be constructed by rectifying a cube. It can also be created by rectifying an octahedron, or by cantellating a tetrahedron (when considered with this symmetry, it can be called a rhombitetratetrahedron).

As a rectified octahedron, it has the same symmetry group as the octahedron, namely octahedral symmetry (Oh).

The dual of the cuboctahedron is called a rhombic dodecahedron.

The Bowers acronym for the cuboctahedron is co.

## Structure and Sections

On each vertex of the cuboctahedron, two triangles and two squares join.

### Hypervolumes

• vertex count = $12$
• edge length = $24 l$
• surface area = $\left( 6 + 2\sqrt{3} \right) l^2$
• surcell volume = $\frac{5}{3} \sqrt{2} l^3$

### Subfacets

Regular
$t_0 \{4,3\}$
Rectified
$t_1 \{4,3\}$
Birectified
$t_2 \{4,3\}$
Truncated
$t_{0,1} \{4,3\}$
Bitruncated
$t_{1,2} \{4,3\}$
Cantellated
$t_{0,2} \{4,3\}$
Cantitruncated
$t_{0,1,2} \{4,3\}$
Cube Cuboctahedron Octahedron Truncated cube Truncated octahedron Rhombicuboctahedron Great rhombicuboctahedron
Regular
$t_0 \{3,3\}$
Rectified
$t_1 \{3,3\}$
Birectified
$t_2 \{3,3\}$
Truncated
$t_{0,1} \{3,3\}$
Bitruncated
$t_{1,2} \{3,3\}$
Cantellated
$t_{0,2} \{3,3\}$
Cantitruncated
$t_{0,1,2} \{3,3\}$
Tetrahedron Octahedron Tetrahedron Truncated tetrahedron Truncated tetrahedron Cuboctahedron Truncated octahedron
$t_1 \{2,4\}$ $t_1 \{3,4\}$ $t_1 \{4,4\}$ $t_1 \{5,4\}$ $t_1 \{6,4\}$ ... $t_1 \{\aleph_0,3\}$
Square dihedron Cuboctahedron Square tiling Tetrapentagonal tiling Tetrahexagonal tiling ... Tetrapeirogonal tiling
$t_1 \{2,3\}$ $t_1 \{3,3\}$ $t_1 \{4,3\}$ $t_1 \{5,3\}$ $t_1 \{6,3\}$ $t_1 \{7,3\}$ $t_1 \{8,3\}$ ... $t_1 \{\aleph_0,3\}$
Trigonal dihedron Octahedron Cuboctahedron Icosidodecahedron Trihexagonal tiling Triheptagonal tiling Trioctagonal tiling ... Triapeirogonal tiling
$t_{0,2} \{2,3\}$ $t_{0,2} \{3,3\}$ $t_{0,2} \{4,3\}$ $t_{0,2} \{5,3\}$ $t_{0,2} \{6,3\}$ $t_{0,2} \{7,3\}$ $t_{0,2} \{8,3\}$ ... $t_{0,2} \{\aleph_0,3\}$
Triangular prism Cuboctahedron Rhombicuboctahedron Rhombicosidodecahedron Rhombitrihexagonal tiling Rhombitriheptagonal tiling Rhombitrioctagonal tiling ... Rhombitriapeirogonal tiling