Uniform tiling symmetry mutations

Orbifolds 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. This table is not complete for possible hyperbolic orbifolds.

{{Regular hosohedral tilings}}

{{Regular_dihedral_tilings}}

{{Antiprism tilings}}

{{Triangular regular tiling}}

{{Order-3 tiling table}}

{{Truncated figure1 table}}

{{Truncated figure2 table}}

{{Quasiregular3 table}}

{{Dual quasiregular3 table}}

{{Expanded table}}

{{Dual expanded table}}

{{Omnitruncated table}}

{{Snub table}}

{{Square regular tiling table}}

{{Order-4_regular_tilings}}

{{Quasiregular4 table}}

{{Dual quasiregular4 table}}

{{Truncated figure3 table}}

{{Truncated figure4 table}}

{{Expanded4 table}}

{{Omnitruncated4 table}}

{{Snub4 table}}

{{Pentagonal regular tilings}}

{{Hexagonal regular tilings}}

{{Octagonal regular tilings}}

{{reflist}}

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, {{ISBN|978-1-56881-220-5}} [https://web.archive.org/web/20100919143320/https://akpeters.com/product.asp?ProdCode=2205]
• [http://www.crystallography.fr/mathcryst/pdf/Leuven_Hyde_slides.pdf From hyperbolic 2-space to Euclidean 3-space: Tilings and patterns via topology] Stephen Hyde

Category:Polyhedra

Category:Euclidean tilings

Category:Hyperbolic tilings