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 also rectangles.
| 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 | ||||||
The rhombic triacontahedron forms the convex hull of one projection of a 6-cube to 3 dimensions.
The 3D basis vectors are:
|
Shown with inner edges hidden |
| There are 64 vertices and 192 unit length edges forming pentagonal symmetry along specific axis (as well as hexagonal symmetries on other axis). | |
Read more about this topic: Rhombic Triacontahedron
Famous quotes containing the word related:
“One does not realize the historical sensation as a re-experiencing, but as an understanding that is closely related to the understanding of music, or rather of the world by means of music.”
—Johan Huizinga (1872–1945)