Rhombic Dodecahedron - Related Polyhedra

Related Polyhedra

This polyhedron is a part of a sequence of rhombic polyhedra and tilings with Coxeter group symmetry. The cube can be seen as a rhombic hexahedron where the rhombi are squares.

Spherical polyhedra Euclidean tiling Hyperbolic tiling
Spherical/planar
symmetry
*332

Td
*432

Oh
*532

Ih
*632

P6m
*732
*832
Rhombic
figures

Cube

Rhombic dodecahedron

Rhombic triacontahedron

Rhombille
Face configuration V3.3.3.3 V3.4.3.4 V3.5.3.5 V3.6.3.6 V3.7.3.7 V3.8.3.8
Coxeter diagram
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} h{4,3} h1,2{4,3}
Duals to uniform polyhedra
{3,4} f0,1{4,3} f1{4,3} f0,1{3,4} {4,3} f0,2{4,3} f0,1,2{4,3} ds{4,3} hf{4,3} hf1,2{4,3}
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}
Uniform duals
{3,3} f0,1{3,3} f1{3,3} f1,2{3,3} f2{3,3} f0,2{3,3} f0,1,2{3,3} {5,3}

Similarly it relates to the infinite series of tilings with the face configurations V3.2n.3.2n, the first in the Euclidean plane, and the rest in the hyperbolic plane.


V3.4.3.4
(Drawn as a net)

V3.6.3.6
Euclidean plane tiling
Rhombille tiling

V3.8.3.8
Hyperbolic plane tiling
(Drawn in a Poincaré disk model)

Read more about this topic:  Rhombic Dodecahedron

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