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.
Dynkin based symbols of the cuboctahedron include:
- o4x3o (full symmetry)
- x3o3x (rhombitetratetrahedron)
- xox4oqo&#xt (square symmetry)
- xxo3oxx&#xt (triangular gyrobicupola)
- oxuxo oqoqo&#xt (vertex first)
- qo xo4oq&#zx (square prism symmetry)
- qqo qoq oqq&#zx (block symmetry)
Structure and Sections
- Vertex radius:
- Edge radius:
- Triangle radius:
- Square radius:
- Dihedral angle:
The vertex coordinates of a cuboctahedron with length 2 are all permuations of (±√2,±√2,0).
- Dual: Rhombic dodecahedron
- Vertex figure: Rectangle, edges 1 and
- Caps: Triangular cupola (triangle first)
- Gyrations: Triangular orthobicupola
- Regiment members: 3 (other members: Octahemioctahedron, Cubohemioctahedron)
|Regular ||Rectified ||Birectified ||Truncated ||Bitruncated ||Cantellated ||Cantitruncated ||Cube||Cuboctahedron||Octahedron||Truncated cube||Truncated octahedron||Rhombicuboctahedron||Great rhombicuboctahedron|
|Regular ||Rectified ||Birectified ||Truncated ||Bitruncated ||Cantellated ||Cantitruncated ||Tetrahedron||Octahedron||Tetrahedron||Truncated tetrahedron||Truncated tetrahedron||Cuboctahedron||Truncated octahedron|
|...||Square dihedron||Cuboctahedron||Square tiling||Tetrapentagonal tiling||Tetrahexagonal tiling||...||Tetrapeirogonal tiling|
|...||Trigonal dihedron||Octahedron||Cuboctahedron||Icosidodecahedron||Trihexagonal tiling||Triheptagonal tiling||Trioctagonal tiling||...||Triapeirogonal tiling|
|...||Triangular prism||Cuboctahedron||Rhombicuboctahedron||Rhombicosidodecahedron||Rhombitrihexagonal tiling||Rhombitriheptagonal tiling||Rhombitrioctagonal tiling||...||Rhombitriapeirogonal tiling|