Triangular tiling
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees. The triangular tiling has Schläfli symbol of {3,6}.
| Triangular tiling | |
|---|---|
| Type | Regular tiling |
| Vertex configuration | 3.3.3.3.3.3 (or 36) |
| Face configuration | V6.6.6 (or V63) |
| Schläfli symbol(s) | {3,6} {3[3]} |
| Wythoff symbol(s) | 6 | 3 2 3 | 3 3 | 3 3 3 |
| Coxeter diagram(s) | = |
| Symmetry | p6m, [6,3], (*632) |
| Rotation symmetry | p6, [6,3]+, (632) p3, [3[3]]+, (333) |
| Dual | Hexagonal tiling |
| Properties | Vertex-transitive, edge-transitive, face-transitive |
English mathematician John Conway called it a deltille, named from the triangular shape of the Greek letter delta (Δ). The triangular tiling can also be called a kishextille by a kis operation that adds a center point and triangles to replace the faces of a hextille.
It is one of three regular tilings of the plane. The other two are the square tiling and the hexagonal tiling.