Related Polyhedra and Tilings
This tiling is topologically related as a part of sequence of regular polyhedra and tilings, extending into the hyperbolic plane: {4,p}, p=3,4,5...
{4,3} |
{4,4} |
{4,5} |
{4,6} |
{4,7} |
{4,8} |
... | {4,∞} |
This tiling is also topologically related as a part of sequence of regular polyhedra and tilings with four faces per vertex, starting with the octahedron, with Schläfli symbol {n,4}, and Coxeter diagram, with n progressing to infinity.
| Spherical | Euclidean | Hyperbolic tilings | ||||||
|---|---|---|---|---|---|---|---|---|
{2,4} |
{3,4} |
{4,4} |
{5,4} |
{6,4} |
{7,4} |
{8,4} |
... | {∞,4} |
| Symmetry *4n2 |
Spherical | Euclidean | Hyperbolic... | ||||
|---|---|---|---|---|---|---|---|
| *342 |
*442 |
*542 |
*642 |
*742 |
*842 |
*∞42 |
|
| Coxeter | |||||||
| Quasiregular figures configuration |
4.3.4.3 |
4.4.4.4 |
4.5.4.5 |
4.6.4.6 |
4.7.4.7 |
4.8.4.8 |
4.∞.4.∞ |
| Dual figures | |||||||
| Coxeter | |||||||
| Dual (rhombic) figures configuration |
V4.3.4.3 |
V4.4.4.4 |
V4.5.4.5 |
V4.6.4.6 |
V4.7.4.7 |
V4.8.4.8 |
V4.∞.4.∞ |
| Symmetry , (*n42) |
Spherical | Euclidean | Hyperbolic tiling | ||||
|---|---|---|---|---|---|---|---|
| *342 |
*442 |
*542 |
*642 |
*742 |
*842 |
*∞42 |
|
| Quasiregular figures |
|||||||
| Coxeter Schläfli |
t0,2{3,4} |
t0,2{4,4} |
t0,2{5,4} |
t0,2{6,4} |
t0,2{7,4} |
t0,2{8,4} |
t0,2{∞,4} |
| Dual (rhombic) figures configuration |
V3.4.4.4 |
V4.4.4.4 |
5.4.4.4 |
V6.4.4.4 |
V7.4.4.4 |
V8.4.4.4 |
V∞.4.4.4 |
| Coxeter | |||||||
Read more about this topic: Square Tiling
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