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Truncated Order-6 Pentagonal Tiling
In geometry, the truncated order-6 pentagonal tiling is a Uniform tilings in hyperbolic plane, uniform tiling of the Hyperbolic geometry, hyperbolic plane. It has Schläfli symbol of t1,2. Uniform colorings Symmetry The dual of this tiling represents the fundamental domains of the *553 symmetry. There are no mirror removal subgroups of [(5,5,3)], but this symmetry group can be doubled to 652 symmetry by adding a bisecting mirror to the fundamental domains. Related polyhedra and tiling References * John Horton Conway, John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, ''The Symmetries of Things'' 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations) * See also *Square tiling *Tilings of regular polygons *List of uniform planar tilings *List of regular polytopes External links * * Hyperbolic and Spherical Tiling Gallery * [http://www.plunk.org/~hatch/HyperbolicTesselations Hyperbolic Planar Tessellations, Don Hatch] {{Tessellation Hyperbolic tilings ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
