| 词条 | Truncated triheptagonal tiling | |||
| 释义 |
In geometry, the truncated triheptagonal tiling is a semiregular tiling of the hyperbolic plane. There are one square, one hexagon, and one tetradecagon (14-sides) on each vertex. It has Schläfli symbol of tr{7,3}. Uniform coloringsThere is only one uniform coloring of a truncated triheptagonal tiling. (Naming the colors by indices around a vertex: 123.) SymmetryEach triangle in this dual tiling, order 3-7 kisrhombille, represent a fundamental domain of the Wythoff construction for the symmetry group [7,3].
Related polyhedra and tilingsThis tiling can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin diagram {{CDD|node_1|p|node_1|3|node_1}}. For p < 6, the members of the sequence are omnitruncated polyhedra (zonohedrons), shown below as spherical tilings. For p > 6, they are tilings of the hyperbolic plane, starting with the truncated triheptagonal tiling. {{Omnitruncated table}}From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling. Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms. {{Heptagonal tiling table}}See also{{Commons category|Uniform tiling 4-6-14}}
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External links
4 : Hyperbolic tilings|Isogonal tilings|Semiregular tilings|Truncated tilings |
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