Schläfli symbol

The Schläfli symbol is named after the Swiss mathematician Ludwig Schläfli, is used in the mold in order to describe regular polygons, polyhedra and other polyhedron in higher dimensions.

If all is the symbol describes a regular polygon. If a non- reduced fraction necessary, then it describes a star.

The symbol describes a tiling by regular corner, which indicates how many such polygons meet at each corner.

The inversion of a Schläfli symbol provides the corresponding dual polygon.

Examples

Polygons and stars

Denotes a corner.

Called the pentagram.

And denote the Heptagramme and.

Platonic Solids

Denotes the self-dual tetrahedron.

Referred to the octahedron, the inversion of the dual cube to an octahedron.

Referred to the icosahedron, the inversion of the dual icosahedron to dodecahedron.

Platonic flooring

Denotes the Dreieckparkettierung, the inversion of the dual Dreieckparkettierung Sechseckparkettierung.

Denotes the self-dual Quadratparkettierung.

Kepler - Poinsot body

Called the Great icosahedron, the inversion of the dual to the Great Icosahedron Great Sterndodekaeder.

Called the Great dodecahedron, the inversion of the dual to the Great dodecahedron Small Sterndodekaeder.

Four-dimensional body

Denotes the Pentachoron,

The four-dimensional cube, the dual to the regular 16- Zeller ( Hexadekachor )

The regular 24 - Zeller ( Ikositetrachor )

The regular 120 - Zeller, the dual to the regular 600 - Zeller.