sentences:  A uniform 9-polytope is one which is vertex-transitive, and constructed from uniform 8-polytope facets.Regular 9-polytopes can be represented by the Schläfli symbol {p,q,r,s,t,u,v,w}, with w {p,q,r,s,t,u,v} 8-polytope facets around each peak.There are exactly three such convex regular 9-polytopes