Wikipedia
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:
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Uniform polytope#Truncation_operators
- For regular polygons: An ordinary truncation, t{p} = t{p} = {2p}.
- Coxeter-Dynkin diagram
- For uniform polyhedra (3-polytopes): A cantitruncation (great rhombation), t{p,q} = tr{p,q}. (Application of both cantellation and truncation operations)
- Coxeter-Dynkin diagram:
- For Uniform 4-polytopes: A runcicantitruncation (great prismation), t{p,q,r}. (Application of runcination, cantellation, and truncation operations)
- Coxeter-Dynkin diagram: , ,
- For uniform polytera (5-polytopes): A steriruncicantitruncation (great cellation), t{p,q,r,s}. (Application of sterication, runcination, cantellation, and truncation operations)
- Coxeter-Dynkin diagram: , ,
- For uniform n-polytopes: t{p,p,...,p}.
- For regular polygons: An ordinary truncation, t{p} = t{p} = {2p}.