Triakis triangular tiling
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| Triakis triangular tiling | |
|---|---|
 |
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| Type | Semiregular tiling |
| Faces | triangle |
| Edges | Infinite |
| Vertices | Infinite |
| Face configuration | V3.12.12 |
| Symmetry group | p6m |
| Dual | Truncated hexagonal tiling |
| Properties | face-transitive |
In geometry, the Triakis triangular tiling is a tiling of the Euclidean plane. It is an equilateral triangular tiling with each triangle divided into three triangles from the center point.
It is labeled V3.12.12 because each isosceles triangle face has two types of vertices: one with 3 triangles, and two with 12 triangles. It is the dual tessellation of the truncated hexagonal tiling which has one triangle and two dodecagons at each vertex.
It is topologically related to this polyhedra sequence, and continue into hyperbolic plane tilings.
- V3.6.6 - Triakis tetrahedron dual of Truncated tetrahedron
- V3.8.8 - Triakis octahedron dual of Truncated cube
- V3.10.10 - Triakis icosahedron dual of Truncated dodecahedron
 V3.6.6 |
 V3.8.8 |
 V3.10.10 |
 V3.12.12 |
 V3.14.14 |
[edit] See also
[edit] References
- Grünbaum, Branko ; and Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman. ISBN 0-716-71193-1. (Chapter 2.1: Regular and uniform tilings, p.58-65)
- Williams, Robert The Geometrical Foundation of Natural Structure: A Source Book of Design New York: Dover, 1979. p39
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