Schläfli symbol en · NOUN
Etymology
From Schläfli (“a surname”) + symbol, after 19th-century Swiss mathematician Ludwig Schläfli (1814–1895).
Meanings
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A notation that recursively encodes certain properties of a specified regular polytope or tessellation.
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.
2012, John Barnes, Gems of Geometry, 2nd edition, page 79:1995, 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}.
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.
2007, Michael E. Mortenson, chapter L, in Geometric Transformations for 3D Modeling, page 248:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Schläfli symbols | Number=Plur | lexicographic |
Synonyms
Schläfli notation (notation encoding certain properties of a regular polytope or tessellation)
Translations (8)
de Schläfli-Symbol (notation encoding certain properties of a regular polytope or tessellation) · ro simbol Schläfli (notation encoding certain properties of a regular polytope or tessellation) · hu Schläfli-szimbólum (notation encoding certain properties of a regular polytope or tessellation) · ko 슐래플리 기호 (notation encoding certain properties of a regular polytope or tessellation) · it simbolo di Schläfli (notation encoding certain properties of a regular polytope or tessellation) · pl symbol Schläfliego (notation encoding certain properties of a regular polytope or tessellation) · ja シュレーフリ記号 (notation encoding certain properties of a regular polytope or tessellation) · fi Schläflin symboli (notation encoding certain properties of a regular polytope or tessellation)