| 词条 | Uniform tiling symmetry mutations | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 释义 |
In geometry, a symmetry mutation is a mapping of fundamental domains between two symmetry groups.[1] They are compactly expressed in orbifold notation. These mutations can occur from spherical tilings to Euclidean tilings to hyperbolic tilings. Hyperbolic tilings can also be divided between compact, paracompact and divergent cases. The uniform tilings are the simplest application of these mutations, although more complex patterns can be expressed within a fundamental domain. This article expressed progressive sequences of uniform tilings within symmetry families. Mutations of orbifoldsOrbifolds with the same structure can be mutated between different symmetry classes, including across curvature domains from spherical, to Euclidean to hyperbolic. This table shows mutation classes.[1] This table is not complete for possible hyperbolic orbifolds.
*n22 symmetryRegular tilings{{Regular hosohedral tilings}}{{Regular_dihedral_tilings}}Prism tilings{{Prism tilings}}Antiprism tilings{{Antiprism tilings}}*n32 symmetryRegular tilings{{Triangular regular tiling}}{{Order-3 tiling table}}Truncated tilings{{Truncated figure1 table}}{{Truncated figure2 table}}Quasiregular tilings{{Quasiregular3 table}}{{Dual quasiregular3 table}}Expanded tilings{{Expanded table}}{{Dual expanded table}}Omnitruncated tilings{{Omnitruncated table}}Snub tilings{{Snub table}}*n42 symmetryRegular tilings{{Square regular tiling table}}{{Order-4_regular_tilings}}Quasiregular tilings{{Quasiregular4 table}}{{Dual quasiregular4 table}}Truncated tilings{{Truncated figure3 table}}{{Truncated figure4 table}}Expanded tilings{{Expanded4 table}}Omnitruncated tilings{{Omnitruncated4 table}}Snub tilings{{Snub4 table}}*n52 symmetryRegular tilings{{Pentagonal regular tilings}}*n62 symmetryRegular tilings{{Hexagonal regular tilings}}*n82 symmetryRegular tilings{{Octagonal regular tilings}}References1. ^1 Two Dimensional symmetry Mutations by Daniel Huson
3 : Polyhedra|Euclidean tilings|Hyperbolic tilings |
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