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 Subfacets See Also
Regular
t
0
{
4
,
3
}
{\displaystyle t_0 \{4,3\}}
Rectified
t
1
{
4
,
3
}
{\displaystyle t_1 \{4,3\}}
Birectified
t
2
{
4
,
3
}
{\displaystyle t_2 \{4,3\}}
Truncated
t
0
,
1
{
4
,
3
}
{\displaystyle t_{0,1} \{4,3\}}
Bitruncated
t
1
,
2
{
4
,
3
}
{\displaystyle t_{1,2} \{4,3\}}
Cantellated
t
0
,
2
{
4
,
3
}
{\displaystyle t_{0,2} \{4,3\}}
Cantitruncated
t
0
,
1
,
2
{
4
,
3
}
{\displaystyle t_{0,1,2} \{4,3\}}
Cube
Cuboctahedron
Octahedron
Truncated cube
Truncated octahedron
Rhombicuboctahedron
Great rhombicuboctahedron
Regular
t
0
{
3
,
3
}
{\displaystyle t_0 \{3,3\}}
Rectified
t
1
{
3
,
3
}
{\displaystyle t_1 \{3,3\}}
Birectified
t
2
{
3
,
3
}
{\displaystyle t_2 \{3,3\}}
Truncated
t
0
,
1
{
3
,
3
}
{\displaystyle t_{0,1} \{3,3\}}
Bitruncated
t
1
,
2
{
3
,
3
}
{\displaystyle t_{1,2} \{3,3\}}
Cantellated
t
0
,
2
{
3
,
3
}
{\displaystyle t_{0,2} \{3,3\}}
Cantitruncated
t
0
,
1
,
2
{
3
,
3
}
{\displaystyle t_{0,1,2} \{3,3\}}
Tetrahedron
Octahedron
Tetrahedron
Truncated tetrahedron
Truncated tetrahedron
Cuboctahedron
Truncated octahedron
t
1
{
2
,
4
}
{\displaystyle t_{1}\{2,4\}}
t
1
{
3
,
4
}
{\displaystyle t_{1}\{3,4\}}
t
1
{
4
,
4
}
{\displaystyle t_1 \{4,4\}}
t
1
{
5
,
4
}
{\displaystyle t_1 \{5,4\}}
t
1
{
6
,
4
}
{\displaystyle t_{1}\{6,4\}}
...
t
1
{
ℵ
0
,
3
}
{\displaystyle t_{1}\{\aleph _{0},3\}}
Square dihedron
Cuboctahedron
Square tiling
Tetrapentagonal tiling
Tetrahexagonal tiling
...
Tetrapeirogonal tiling
t
1
{
2
,
3
}
{\displaystyle t_1 \{2,3\}}
t
1
{
3
,
3
}
{\displaystyle t_1 \{3,3\}}
t
1
{
4
,
3
}
{\displaystyle t_1 \{4,3\}}
t
1
{
5
,
3
}
{\displaystyle t_1 \{5,3\}}
t
1
{
6
,
3
}
{\displaystyle t_1 \{6,3\}}
t
1
{
7
,
3
}
{\displaystyle t_1 \{7,3\}}
t
1
{
8
,
3
}
{\displaystyle t_1 \{8,3\}}
...
t
1
{
∞
,
3
}
{\displaystyle t_1 \{\infty,3\}}
t
1
{
i
π
λ
,
3
}
{\displaystyle t_1 \{\frac{i\pi}{\lambda},3\}}
Trigonal dihedron
Octahedron
Cuboctahedron
Icosidodecahedron
Trihexagonal tiling
Triheptagonal tiling
Trioctagonal tiling
...
Triapeirogonal tiling
Tripseudogonal tiling
t
0
,
2
{
2
,
3
}
{\displaystyle t_{0,2} \{2,3\}}
t
0
,
2
{
3
,
3
}
{\displaystyle t_{0,2} \{3,3\}}
t
0
,
2
{
4
,
3
}
{\displaystyle t_{0,2} \{4,3\}}
t
0
,
2
{
5
,
3
}
{\displaystyle t_{0,2} \{5,3\}}
t
0
,
2
{
6
,
3
}
{\displaystyle t_{0,2} \{6,3\}}
t
0
,
2
{
7
,
3
}
{\displaystyle t_{0,2} \{7,3\}}
t
0
,
2
{
8
,
3
}
{\displaystyle t_{0,2} \{8,3\}}
...
t
0
,
2
{
∞
,
3
}
{\displaystyle t_{0,2} \{\infty,3\}}
t
0
,
2
{
π
i
λ
,
3
}
{\displaystyle t_{0,2} \{\frac{\pi i}{\lambda},3\}}
Triangular prism
Cuboctahedron
Rhombicuboctahedron
Rhombicosidodecahedron
Rhombitrihexagonal tiling
Rhombitriheptagonal tiling
Rhombitrioctagonal tiling
...
Rhombitriapeirogonal tiling
Rhombitripseudogonal tiling
