Truncated hexagonal tiling
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| Truncated hexagonal tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform |
| Space | Euclidean |
| Notation | |
| Bowers style acronym | Toxat |
| Coxeter diagram | x6x3o (    ) |
| Elements | |
| Faces | 2N triangles, N dodecagons |
| Edges | 3N+6N |
| Vertices | 6N |
| Vertex figure | Isosceles triangle, edge lengths 1, (√2+√6)/2, (√2+√6)/2 |
| Measures (edge length 1) | |
| Vertex density | |
| Related polytopes | |
| Army | Toxat |
| Regiment | Toxat |
| Dual | Triakis triangular tiling |
| Conjugate | Quasitruncated hexagonal tiling |
| Abstract & topological properties | |
| Flag count | 36N |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | V3 |
| Convex | Yes |
| Nature | Tame |
The truncated hexagonal tiling, or toxat, is one of the eleven convex uniform tilings of the Euclidean plane. 1 triangle and 2 dodecagons join at each vertex of this tiling. As its name suggests, it is the truncation of the regular hexagonal tiling.
External links[edit | edit source]
- Klitzing, Richard. "toxat".
- Wikipedia contributors. "Truncated hexagonal tiling".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Hexagonal tiling | hexat | {6,3} | |  |
| Trihexagonal tiling | that | r {6,3} | |  |
| Triangular tiling | trat | {3,6} | |  |
| Truncated hexagonal tiling | toxat | t {6,3} | |  |
| Small rhombitrihexagonal tiling | srothat | rr {6,3} | |  |
| Truncated triangular tiling = Hexagonal tiling | hexat | t {3,6} | |  |
| Great rhombitrihexagonal tiling | grothat | tr {6,3} | |  |
| Snub trihexagonal tiling | snathat | sr {6,3} |  |  |