Omnitruncation

In geometry, an omnitruncation is an operation applied to a regular polytope (or honeycomb) in a Wythoff construction that creates a maximum number of facets. It is represented in a Coxeter–Dynkin diagram with all nodes ringed.

It is a shortcut term which has a different meaning in progressively-higher-dimensional polytopes:

• Uniform polytope#Truncation operators
• For regular polygons: An ordinary truncation, $t_{0,1}\{p\}=t\{p\}=\{2p\}$ .
• Coxeter-Dynkin diagram   • For uniform polyhedra (3-polytopes): A cantitruncation, $t_{0,1,2}\{p,q\}=tr\{pq\}$ . (Application of both cantellation and truncation operations)
• Coxeter-Dynkin diagram:     • For uniform 4-polytopes: A runcicantitruncation, $t_{0,1,2,3}\{p,q,r\}$ . (Application of runcination, cantellation, and truncation operations)
• Coxeter-Dynkin diagram:       ,     ,     • For uniform polytera (5-polytopes): A steriruncicantitruncation, t0,1,2,3,4{p,q,r,s}. $t_{0,1,2,3,4}\{p,q,r,s\}$ . (Application of sterication, runcination, cantellation, and truncation operations)
• Coxeter-Dynkin diagram:         ,       ,     • For uniform n-polytopes: $t_{0,1,...,n-1}\{p_{1},p_{2},...,p_{n}\}$ .