The square tiling is a regular tiling formed of a plane filled with squares. It has a Schläfli symbol of , as four squares join at each vertex. Its bowers acronym is squat.
Colorings
There are nine different uniform colorings of the square tiling (in which the colors around each vertex are the same).
The following numbers label the colors around each vertex clockwise (for example "1212" shows that as you go clockwise around a vertex you find a square with color 1, then color 2, then color 1, then color 2 again, then it repeats).
The nine uniform colorings are:
- 1111 - this is the regular form.
- 1212 - this can be formed from the rectified square tiling, or .
- 1213 - this can be formed as the cantellated square tiling or .
- 1122
- 1234
- 2 types of 1112
- 2 types of 1123
Subfacets
- Infinite points (0D)
- Infinite line segments (1D)
- Infinite squares (2D)
See Also
Regular Hypercubic Tilings
- Apeirogon
- Square tiling
- Cubic honeycomb
- Tesseractic tetracomb
- Penteractic pentacomb
Uniform Shapes with the Same Faces
... | |||||||||
---|---|---|---|---|---|---|---|---|---|
Square dihedron | Cube | Square tiling | Order-5 square tiling | Order-6 square tiling | Order-7 square tiling | Order-8 square tiling | ... | Infinite-order square tiling | Imaginary-order square tiling |
Uniform Shapes with the Same Faces per Vertex
... | |||||||||
---|---|---|---|---|---|---|---|---|---|
Square hosohedron | Octahedron | Square tiling | Order-4 pentagonal tiling | Order-4 hexagonal tiling | Order-4 heptagonal tiling | Order-4 octagonal tiling | ... | Order-4 apeirogonal tiling | Order-4 pseudogonal tiling |
Uniform Tilings
Regular |
Rectified |
Birectified |
Truncated |
Bitruncated |
Cantellated |
Cantitruncated |
---|---|---|---|---|---|---|
Square tiling | Square tiling | Square tiling | Truncated square tiling | Truncated square tiling | Square tiling | Truncated square tiling |