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 | ||||||
| {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} |
| {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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