Uniform 10-polytope - Regular 10-polytopes

Regular 10-polytopes

Regular 10-polytopes can be represented by the Schläfli symbol {p,q,r,s,t,u,v,w,x}, with x {p,q,r,s,t,u,v,w} 9-polytope facets around each peak.

There are exactly three such convex regular 10-polytopes:

1. {3,3,3,3,3,3,3,3,3} - 10-simplex
2. {4,3,3,3,3,3,3,3,3} - 10-cube
3. {3,3,3,3,3,3,3,3,4} - 10-orthoplex

There are no nonconvex regular 10-polytopes.