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- Uniform_tiling abstract "In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-uniform.Uniform tilings can exist in both the Euclidean plane and hyperbolic plane. Uniform tilings are related to the finite uniform polyhedra which can be considered uniform tilings of the sphere.Most uniform tilings can be made from a Wythoff construction starting with a symmetry group and a singular generator point inside of the fundamental domain. A planar symmetry group has a polygonal fundamental domain and can be represented by the group name represented by the order of the mirrors in sequential vertices. A fundamental domain triangle is (p q r), and a right triangle (p q 2), where p, q, r are whole numbers greater than 1. The triangle may exist as a spherical triangle, a Euclidean plane triangle, or a hyperbolic plane triangle, depending on the values of p, q and r.There are a number of symbolic schemes for naming these figures, from a modified Schläfli symbol for right triangle domains: (p q 2) → {p, q}. The Coxeter-Dynkin diagram is a triangular graph with p, q, r labeled on the edges. If r = 2, the graph is linear since order-2 domain nodes generate no reflections. The Wythoff symbol takes the 3 integers and separates them by a vertical bar (|). If the generator point is off the mirror opposite a domain node, it is given before the bar. Finally tilings can be described by their vertex configuration, the sequence of polygons around each vertex.All uniform tilings can be constructed from various operations applied to regular tilings. These operations as named by Norman Johnson are called truncation (cutting vertices), rectification (cutting vertices until edges disappear), and Cantellation (cutting edges). Omnitruncation is an operation that combines truncation and cantellation. Snubbing is an operation of Alternate truncation of the omnitruncated form. (See Uniform_polyhedron#Wythoff_construction_operators for more details.)".
- Uniform_tiling thumbnail Tiling_Dual_Semiregular_V4-8-8_Tetrakis_Square-2-color-zoom.svg?width=300.
- Uniform_tiling wikiPageExternalLink sici?sici=0080-4614%2819540513%29246%3A916%3C401%3AUP%3E2.0.CO%3B2-4.
- Uniform_tiling wikiPageExternalLink tilings.html.
- Uniform_tiling wikiPageExternalLink tessel.htm.
- Uniform_tiling wikiPageExternalLink www.tess-elation.co.uk.
- Uniform_tiling wikiPageExternalLink uniftil.htm.
- Uniform_tiling wikiPageExternalLink ue2.
- Uniform_tiling wikiPageID "12126635".
- Uniform_tiling wikiPageRevisionID "578082736".
- Uniform_tiling hasPhotoCollection Uniform_tiling.
- Uniform_tiling title "Uniform tessellation".
- Uniform_tiling urlname "UniformTessellation".
- Uniform_tiling subject Category:Tessellation.
- Uniform_tiling comment "In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-uniform.Uniform tilings can exist in both the Euclidean plane and hyperbolic plane. Uniform tilings are related to the finite uniform polyhedra which can be considered uniform tilings of the sphere.Most uniform tilings can be made from a Wythoff construction starting with a symmetry group and a singular generator point inside of the fundamental domain.".
- Uniform_tiling label "Uniform tiling".
- Uniform_tiling sameAs 고른_타일링.
- Uniform_tiling sameAs m.04f4vk2.
- Uniform_tiling sameAs Q7885119.
- Uniform_tiling sameAs Q7885119.
- Uniform_tiling wasDerivedFrom Uniform_tiling?oldid=578082736.
- Uniform_tiling depiction Tiling_Dual_Semiregular_V4-8-8_Tetrakis_Square-2-color-zoom.svg.
- Uniform_tiling isPrimaryTopicOf Uniform_tiling.
