A Schläfli symbol is a symbol of the form 
used to describe regular
polygons, regular polyhedra, and their
higher-dimensional counterparts.
The symbol 
denotes a regular polygon with 
sides for an integer 
. A star polygon
has symbol 
, where 
and 
are relatively prime positive integers with 
. It is formed by joining every 
th point among 
equally spaced points on a circle.
The number 
is its polygon density. For example, 
is the pentagram.
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 give Schläfli symbols for several star polygons and polytopes.
| star polygon | symbol |
| pentagram |  |
| octagram |  |
| decagram |  |
| dodecagram |  |
-simplex
-cross polytope
-hypercube
