Related Polyhedra and Tilings
The truncated square tiling is topologically related as a part of sequence of uniform polyhedra and tilings with vertex figures 4.2n.2n, extending into the hyperbolic plane:
| Symmetry *n42 |
Spherical | Euclidean | Hyperbolic... | |||||
|---|---|---|---|---|---|---|---|---|
| *242 D4h |
*342 Oh |
*442 P4m |
*542 |
*642 |
*742 |
*842 ... |
*∞42 |
|
| Truncated figures |
4.4.4 |
4.6.6 |
4.8.8 |
4.10.10 |
4.12.12 |
4.14.14 |
4.16.16 |
4.∞.∞ |
| Coxeter Schläfli |
t1,2{4,2} |
t1,2{4,3} |
t1,2{4,4} |
t1,2{4,5} |
t1,2{4,6} |
t1,2{4,7} |
t1,2{4,8} |
t1,2{4,∞} |
| Uniform dual figures | ||||||||
| n-kis figures |
V4.4.4 |
V4.6.6 |
V4.8.8 |
V4.10.10 |
V4.12.12 |
V4.14.14 |
V4.16.16 |
V4.∞.∞ |
| Coxeter | ||||||||
The Pythagorean tiling alternates large and small squares, and may be seen as topologically identical to the truncated square tiling. The squares are rotated 45 degrees and octagons are distorted into squares with mid-edge vertices.
| Variations on this pattern are often called Mediterranean patterns, shown in stone tiles like this one with smaller squares and diagonally aligned with the borders. | Pythagorean tilings | This weaving pattern has the same topology as well, with octagons flattened into 3 by 1 rectangles | |
The 3-dimensional bitruncated cubic honeycomb projected into the plane shows two copies of a truncated tiling. In the plane it can be represented by a compound tiling:
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Read more about this topic: Truncated Square Tiling
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