The Schläfli symbol is a recursive description, starting with {p} for a p-sided regular polygon that is convex. For example, {3} is an equilateral triangle, {4} is a See more

Schläfli's work was almost unknown in his lifetime, and his notation for describing polytopes was rediscovered independently by several others. In particular, Thorold Gosset rediscovered … See more

• Coxeter, Harold Scott MacDonald (1973) [1948]. Regular Polytopes (3rd ed.). Dover Publications. pp. 14, 69, 149. ISBN 0-486-61480-8. OCLC 798003. Regular Polytopes. See more

A regular polytope has a regular vertex figure. The vertex figure of a regular polytope {p,q,r,...,y,z} is {q,r,...,y,z}.
Regular polytopes can have star polygon elements, like the See more

Symmetry groups
Schläfli symbols are closely related to (finite) reflection symmetry groups, which correspond precisely to the finite Coxeter groups and are specified with the same indices, but square brackets instead [p,q,r,...]. Such … See more

• Weisstein, Eric W. "Schläfli Symbol". MathWorld. Retrieved December 28, 2019.
• Starck, Maurice (April 13, 2012). "Polyhedral Names and Notations". A Ride Through the Polyhedra World. Retrieved December 28, 2019. See more