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Schlafli's Symbol

This is the most widespread of constructions, and applies only to regular figures.


A regular polyhderon is made up from regular polygons of one kind, with a constant number at a corner. A regular polychora is done in the same manner, with polyhedra of one kind, the same at each edge.

Th. Gosset uses the vertex figure, building them up, eg "pentagon-edged tetrahedron"


The notation for the polygons is simply the number of sides it has, eg 3 for a triangle.

For a polyhedron the notation is to use two numbers like {p,q}. This symbol can be read as p-gons, q at a corner. So, the dodecahedron is {5,3}, this means pentagons, three at a corner.

For the polychora, the notation uses three numbers, eg {p,q,r}. This is read as {p,q}, r at an edge.


There are not a lot of regular figures past two dimensions. In three dimensions, there are just five (the Platonic figures), and in four, there are just six. Thereafter, there are just three.

The uniform figures are made by applying the Stott-style variations to the regular figures.

Copyright 2002 Wendy Krieger

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