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
Famous quotes containing the word related:
“Just as a new scientific discovery manifests something that was already latent in the order of nature, and at the same time is logically related to the total structure of the existing science, so the new poem manifests something that was already latent in the order of words.”
—Northrop Frye (b. 1912)
Related Phrases
Related Words