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- The symbol denotes a tessellation of regular -gons, with of them surrounding each polytope vertex. The Schläfli symbol can also be used to describe Platonic solids and Kepler-Poinsot polyhedra, and a generalized version describes quasiregular polyhedra and Archimedean solids.mathworld.wolfram.com/SchlaefliSymbol.html
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Schläfli symbol - Wikipedia
The Schläfli symbol of a regular polyhedron is {p, q} if its faces are p -gons, and each vertex is surrounded by q faces (the vertex figure is a q -gon). For example, {5,3} is the regular dodecahedron. It has pentagonal (5 edges) faces, and 3 pentagons around each vertex. See more
In geometry, the Schläfli symbol is a notation of the form $${\displaystyle \{p,q,r,...\}}$$ that defines regular polytopes and tessellations.
The Schläfli symbol is named after the 19th-century Swiss … See moreA regular polytope has a regular vertex figure. The vertex figure of a regular polytope {p,q,r,...,y,z} is {q,r,...,y,z}.
Regular polytopes can have star polygon elements, like the See moreSymmetry groups
Schläfli symbols are closely related to (finite) reflection symmetry groups, which correspond precisely to the finite Coxeter groups and are specified with the same indices, but square brackets instead [p,q,r,...]. Such … See more• Weisstein, Eric W. "Schläfli Symbol". MathWorld. Retrieved December 28, 2019.
• Starck, Maurice (April 13, 2012). "Polyhedral Names and Notations". A Ride Through the Polyhedra World. Retrieved December 28, 2019. See moreThe Schläfli symbol is a recursive description, starting with {p} for a p-sided regular polygon that is convex. For example, {3} is an equilateral triangle, {4} is a See more
Schläfli's work was almost unknown in his lifetime, and his notation for describing polytopes was rediscovered independently by several others. In particular, Thorold Gosset rediscovered … See more
• Coxeter, Harold Scott MacDonald (1973) [1948]. Regular Polytopes (3rd ed.). Dover Publications. pp. 14, 69, 149. ISBN 0-486-61480-8. OCLC 798003. Regular Polytopes. See more
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WEBOct 1, 2024 · A tiling of regular polygons (in two dimensions), polyhedra (three dimensions), or polytopes ( dimensions) is called a tessellation. Tessellations can be specified using a Schläfli symbol.
Star polygon - Wikipedia
WEBIn geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general …
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