Schläfli symbol

English Etymology From en Schläfli a surname + en symbol, after 19th-century Swiss mathematician Ludwig Schläfli (1814–1895). Noun en geometry A notation that recursively encodes certain properties of a specified regular polytope or tessellation. en Higher-dimensional geometry 1995, Unnamed translator, E. B. Vinberg, Polynomial Group, article in M. Hazewinkel (editor), Encyclopaedia of Mathematics, Volume 4: Monge–Ampère Equation — Rings and Algebras, 2013, International Edition, page 481, The three-dimensional regular polytopes (Platonic solids) have the following Schläfli symbols: the tetrahedron — {3, 3}, the cube — {4, 3}, the octahedron — {3, 4} — the dodecahedron — {5, 3}, and the icosahedron — {3, 5}. en 2007 Michael E. Mortenson Geometric Transformations for 3D Modeling l 248 https://books.google.com.au/books?id=D8GjBgAAQBAJ&pg=PA248&dq=%22S%C3%A4fli+symbol%22%7C%22Schl%C3%A4fli+symbols%22&hl=en&sa=X&ved=0ahUKEwi7wKPv59nMAhXCGqYKHQQuBXYQ6AEIdzAP#v=onepage&q=%22Schl%C3%A4fli%20symbol%22%7C%22Schl%C3%A4fli%20symbols%22&f=false For the regular tiling of squares the Schläfli symbol is {4,4}, indicating that there are four squares surrounding each vertex. And for the regular tiling of hexagons the Schläfli symbol is {6,3}, indicating that there are three hexagons surrounding each vertex. en 2012 John Barnes Gems of Geometry 2nd https://books.google.com.au/books?id=7YCUBUd-4BQC&pg=PA79&dq=%22Schl%C3%A4fli+symbol%22%7C%22Schl%C3%A4fli+symbols%22&hl=en&sa=X&ved=0ahUKEwi7wKPv59nMAhXCGqYKHQQuBXYQ6AEIsQEwGg#v=onepage&q=%22Schl%C3%A4fli%20symbol%22%7C%22Schl%C3%A4fli%20symbols%22&f=false 79 The 24-cell has has 24 octahedral cells, 24 vertices, 96 triangular faces and 96 edges. Its Schläfli symbol is {3, 4, 3} from which we see that the vertex figure is a cube. Synonyms notation encoding certain properties of a regular polytope or tessellation Schläfli notation Translations notation encoding certain properties of a regular polytope or tessellation Finnish: fi Schläflin symboli German: de Schläfli-Symbol n Hungarian: hu Schläfli-szimbólum Italian: it simbolo di Schläfli m Japanese: ja シュレーフリ記号 シュレーフリきごう, Shurēfuri kigō Korean: ko 슐래플리 기호 Polish: pl symbol Schläfliego m-in Romanian: ro simbol Schläfli n en Tesselation en eponyms