In geometry, the Wythoff symbol is a notation representing a Wythoff construction of a uniform polyhedron or plane tiling within a Schwarz triangle. It...
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grouped by the Wythoff symbol. All the faces are identical, each edge is identical and each vertex is identical. They all have a Wythoff symbol of the form...
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A vertex is placed at the point A. This produces a polyhedron with Wythoff symbol a|b c, where a equals π divided by the angle of the triangle at A, and...
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figure. The nine forms, listed with their Wythoff symbols and vertex configurations are: Note that Wythoff's kaleidoscopic construction generates the nonorientable...
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There are different notations for expressing these uniform solutions, Wythoff symbol, Coxeter diagram, and Coxeter's t-notation. Simple tiles are generated...
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sections. All reflectional forms can be made by Wythoff constructions, represented by Wythoff symbols, or Coxeter-Dynkin diagrams, each operating upon...
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Quasiregular polyhedron (section Wythoff construction)
triangular faces. Coxeter defines a quasiregular polyhedron as one having a Wythoff symbol in the form p | q r, and it is regular if q=2 or q=r. The Coxeter-Dynkin...
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only its Wythoff symbol. The 57 nonprismatic nonconvex forms, with exception of the great dirhombicosidodecahedron, are compiled by Wythoff constructions...
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hexagon passing through the origin The Wythoff symbol relates the polyhedron to spherical triangles. Wythoff symbols are written p|q r, p q|r, p q r| where...
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geometry, Wythoff is known for the Wythoff construction of uniform tilings and uniform polyhedra and for the Wythoff symbol used as a notation for these geometric...
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polyhedron that cannot be made by the Wythoff construction from a spherical triangle. It has a special Wythoff symbol | 3⁄2 5⁄3 3 5⁄2, relating it to a spherical...
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by the wallpaper group p6mm, (*632), and the tiling can be derived as a Wythoff construction within the reflectional fundamental domains of this group...
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domain mirrors meeting at 90 degrees generate no new mirrors). The Wythoff symbol takes the three integers and separates them by a vertical bar (|). If...
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plane. With orbifold notation symmetry of *n32 all of these tilings are Wythoff constructions within a fundamental domain of symmetry, with generator points...
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equivalent constructions, for example Wythoff symbol 3 | 3 5⁄4 gives Coxeter diagram = . It has extended Schläfli symbol a{5⁄2,3} or c{3,5⁄2}, as an altered...
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honeycomb Convex uniform honeycombs in hyperbolic space Wythoff construction and Wythoff symbol Hall, Brian C. (2003), Lie Groups, Lie Algebras, and Representations:...
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colorings of a hexagonal tiling, all generated from reflective symmetry of Wythoff constructions. The (h,k) represent the periodic repeat of one colored tile...
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square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex. Conway called it...
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vertices. Its vertex figure is a crossed quadrilateral. It is given Wythoff symbol 4⁄3 4 | 3, although that is a double-covering of this figure. A nonconvex...
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triangle, two squares, and one hexagon on each vertex. It has Schläfli symbol of rr{3,6}. John Conway calls it a rhombihexadeltille. It can be considered...
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notation eD or aaD Schläfli symbols rr{5,3} or r { 5 3 } {\displaystyle r{\begin{Bmatrix}5\\3\end{Bmatrix}}} t0,2{5,3} Wythoff symbol 3 5 | 2 Coxeter diagram...
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at a point occupy a full 360 degrees. The triangular tiling has Schläfli symbol of {3,6}. English mathematician John Conway called it a deltille, named...
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Dodecadodecahedron (section Wythoff constructions)
spherical icosahedron used in construction of geodesic domes. It has four Wythoff constructions between four Schwarz triangle families: 2 | 5 5/2, 2 | 5...
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only non-prismatic uniform polyhedron with an odd number of faces. Its Wythoff symbol is 3/2 3 | 2, but that represents a double covering of the tetrahemihexahedron...
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triangles at the original vertex locations. It is given an extended Schläfli symbol of t{6,3}. Conway calls it a truncated hextille, constructed as a truncation...
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Schläfli symbol a{5,3}, as an altered dodecahedron, and Coxeter diagram or . It is constructed from Schwarz triangle (3 3 5⁄2) with Wythoff symbol 3 | 5⁄2...
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dihedron. A regular dihedron, with Schläfli symbol {n,2}, is made of two regular polygons, each with Schläfli symbol {n}. A spherical dihedron is made of two...
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The Wythoffian uniform polyhedra and tilings can be defined by their Wythoff symbol, which specifies the fundamental region of the object. An extension...
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List of uniform polyhedra by Schwarz triangle (redirect from Uniform star polyhedron/Uniform polyhedra by Wythoff construction)
There are many relationships among the uniform polyhedra. The Wythoff construction is able to construct almost all of the uniform polyhedra from the acute...
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directly from their symmetry groups. They are listed for reference Wythoff's symbol for each of the Platonic solids. The tetrahedron, cube, and octahedron...
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