A symbol of the form 
used to describe regular polygons, polyhedra, and their higher-dimensional counterparts.
The symbol 
denotes a regular polygon for integer 
, or a star polygon for rational
. 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. Higher
dimensional symbols can be used to describe the regular
polychora and polytopes.
The symbol has the particularly nice property that its reversal gives the symbol of the dual polyhedron. The following tables gives Schläfli symbols for several polytopes.
-simplex
-cross polytope
-hypercube
