Truncated Octahedron - Related Polyhedra

Related Polyhedra

The truncated octahedron is one of a family of uniform polyhedra related to the cube and regular octahedron.

Family of uniform octahedral polyhedra
{4,3} t0,1{4,3} t1{4,3} t0,1{3,4} {3,4} t0,2{4,3} t0,1,2{4,3} s{4,3} h0{4,3} h1,2{4,3}

It also exists as the omnitruncate of the tetrahedron family:

Family of uniform tetrahedral polyhedra
{3,3} t0,1{3,3} t1{3,3} t1,2{3,3} t2{3,3} t0,2{3,3} t0,1,2{3,3} s{3,3}
Symmetry Spherical planar Hyperbolic
*232

D3h
*332

Td
*432

Oh
*532

Ih
*632

P6m
*732

*832

*∞32

Order 12 24 48 120
Omnitruncated
figure

4.6.4

4.6.6

4.6.8

4.6.10

4.6.12

4.6.14

4.6.16

4.6.∞
Coxeter
Schläfli

t0,1,2{2,3}

t0,1,2{3,3}

t0,1,2{4,3}

t0,1,2{5,3}

t0,1,2{6,3}

t0,1,2{7,3}

t0,1,2{8,3}

t0,1,2{∞,3}
Omnitruncated
duals

V4.6.4

V4.6.6

V4.6.8

V4.6.10

V4.6.12

V4.6.14
V4.6.16 V4.6.∞
Coxeter

This polyhedron can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin diagram . For p < 6, the members of the sequence are omnitruncated polyhedra (zonohedra), shown below as spherical tilings. For p > 6, they are tilings of the hyperbolic plane, starting with the truncated triheptagonal tiling.

Symmetry Spherical Planar Hyperbolic...
*232

D3h
*332

Td
*432

Oh
*532

Ih
*632

P6m
*732

*832
...
*∞32

Order 12 24 48 120
Truncated
figures

2.6.6

3.6.6

4.6.6

5.6.6

6.6.6

7.6.6

8.6.6

3.4.∞.4
Coxeter
Schläfli

t0,1{3,2}

t0,1{3,3}

t0,1{3,4}

t0,1{3,5}

t0,1{3,6}

t0,1{3,7}

t0,1{3,8}

t0,1{3,∞}
n-kis
figures

V2.6.6

V3.6.6

V4.6.6

V5.6.6

V6.6.6

V7.6.6
Coxeter

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