| 词条 | Order-4 heptagonal tiling | |||||
| 释义 |
In geometry, the order-4 heptagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {7,4}. SymmetryThis tiling represents a hyperbolic kaleidoscope of 7 mirrors meeting as edges of a regular heptagon. This symmetry by orbifold notation is called *2222222 with 7 order-2 mirror intersections. In Coxeter notation can be represented as [1+,7,1+,4], removing two of three mirrors (passing through the heptagon center) in the [7,4] symmetry. The kaleidoscopic domains can be seen as bicolored heptagons, representing mirror images of the fundamental domain. This coloring represents the uniform tiling t1{7,7} and as a quasiregular tiling is called a heptaheptagonal tiling. Related polyhedra and tiling{{Order 7-4 tiling table}}{{Order_7-7_tiling_table}}This tiling is topologically related as a part of sequence of regular tilings with heptagonal faces, starting with the heptagonal tiling, with Schläfli symbol {6,n}, and Coxeter diagram {{CDD|node_1|7|node|n|node}}, progressing to infinity.
This tiling is also topologically related as a part of sequence of regular polyhedra and tilings with four faces per vertex, starting with the octahedron, with Schläfli symbol {n,4}, and Coxeter diagram {{CDD|node_1|n|node|4|node}}, with n progressing to infinity. {{Order-4_regular_tilings}}References
See also{{Commonscat|Order-4 heptagonal tiling}}
External links
6 : Heptagonal tilings|Hyperbolic tilings|Isogonal tilings|Isohedral tilings|Order-4 tilings|Regular tilings |
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