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, t0,1{p} = t{p} = {2p}.
Coxeter-Dynkin diagram
For uniform polyhedra (3-polytopes): A cantitruncation (great rhombation), t0,1,2{p,q} = tr{p,q}. (Application of both cantellation and truncation operations)
Coxeter-Dynkin diagram:
For Uniform 4-polytopes: A runcicantitruncation (great prismation), t0,1,2,3{p,q,r}. (Application of runcination, cantellation, and truncation operations)
Coxeter-Dynkin diagram: , ,
For uniform polytera (5-polytopes): A steriruncicantitruncation (great cellation), t0,1,2,3,4{p,q,r,s}. (Application of sterication, runcination, cantellation, and truncation operations)
Coxeter-Dynkin diagram: , ,
For uniform n-polytopes: t0,1,...,n-1{p1,p2,...,pn}.
