Tetrakis square tiling
From Freepedia
| Tetrakis square tiling | |
|---|---|
| Image:Tetrakis square tiling.png | |
| Type | Semiregular tiling |
| Faces | triangle |
| Edges | Infinite |
| Vertices | Infinite |
| Vertex configuration | V4.8.8 |
| Symmetry group | p4m |
| Dual polyhedron | Truncated square tiling |
| Properties | planar |
In geometry, the tetrakis square tiling is a tiling of the Euclidean plane. It is square tiling with each square divided into four triangles from the center point.
It is labeled V4.8.8 because each isosceles triangle face has two types of vertices: one with 4 triangles, and two with 8 triangles. It is the dual tessellation of the truncated square tiling which has one triangle and two octagons at each vertex.
It is topologically related to the polyhedron tetrakis hexahedron, V4.6.6Image:Tetrakishexahedron.jpg
The symmetry type is:
- with the coloring: cmm; a primitive cell is 8 triangles, a fundamental domain 2 triangles (1/2 for each color)
- with the dark triangles in black and the light ones in white: p4g; a primitive cell is 8 triangles, a fundamental domain 1 triangle (1/2 each for black and white)
- with the edges in black and the interiors in white: p4m; a primitive cell is 2 triangles, a fundamental domain 1/2
