Verse and Dimensions Wikia
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Verse and Dimensions Wikia

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.

Symbols

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

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

Hypervolumes

Subfacets

Radii

  • Vertex radius:
  • Edge radius:
  • Triangle radius:
  • Square radius:

Angles

  • Dihedral angle:

Vertex coordinates

The vertex coordinates of a cuboctahedron with length 2 are all permuations of (±√2,±√2,0).

Related shapes

See Also

Quasiregular polyhedra
thah · co · oho · cho · id · sidhid · seihid · did · sidhei · gidhei · gid · gidhid · geihid · sidtid · gitdid · gidtid
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 Tripseudogonal tiling
...
Triangular prism Cuboctahedron Rhombicuboctahedron Rhombicosidodecahedron Rhombitrihexagonal tiling Rhombitriheptagonal tiling Rhombitrioctagonal tiling ... Rhombitriapeirogonal tiling Rhombitripseudogonal tiling
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