| 词条 | Order-4 pentagonal tiling | ||||||||||
| 释义 |
In geometry, the order-4 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {5,4}. It can also be called a pentapentagonal tiling in a bicolored quasiregular form. SymmetryThis tiling represents a hyperbolic kaleidoscope of 5 mirrors meeting as edges of a regular pentagon. This symmetry by orbifold notation is called *22222 with 5 order-2 mirror intersections. In Coxeter notation can be represented as [5*,4], removing two of three mirrors (passing through the pentagon center) in the [5,4] symmetry. The kaleidoscopic domains can be seen as bicolored pentagons, representing mirror images of the fundamental domain. This coloring represents the uniform tiling t1{5,5} and as a quasiregular tiling is called a pentapentagonal tiling. Related polyhedra and tiling{{Order 5-4 tiling table}}{{Order_5-5_tiling_table}}This tiling is topologically related as a part of sequence of regular polyhedra and tilings with pentagonal faces, starting with the dodecahedron, with Schläfli symbol {5,n}, and Coxeter diagram {{CDD|node_1|5|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}}This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (4n). {{Regular square tiling table}}{{Quasiregular5 table}}References
url=http://www.mathunion.org/ICM/ICM1954.3/Main/icm1954.3.0155.0169.ocr.pdf}}, invited lecture, ICM, Amsterdam, 1954. See also{{Commonscat|Order-4 pentagonal tiling}}
External links
6 : Hyperbolic tilings|Isogonal tilings|Isohedral tilings|Order-4 tilings|Pentagonal tilings|Regular tilings |
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