Omnitruncation
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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.
[edit] See also
- Uniform polytope#Truncation_operators
- For regular polygons: An ordinary truncation, t0,1{p}={2p}.
- For uniform polyhedra (3-polytopes): A cantitruncation, t0,1,2{p, q}. (Application of both cantellation and truncation operations)
- Coxeter-Dynkin diagram:
- Coxeter-Dynkin diagram:
- For uniform polychora (4-polytopes): A runcicantitruncation, t0,1,2,3{p, q,r}. (Application of runcination, cantellation, and truncation operations)
- Coxeter-Dynkin diagram:
- Coxeter-Dynkin diagram:
- For uniform polytera (5-polytopes): A steriruncicantitruncation, t0,1,2,3,4{p, q,r, s}. (Application of sterication, runcination, cantellation, and truncation operations)
- Coxeter-Dynkin diagram:
- Coxeter-Dynkin diagram:
- For uniform n-polytopes: t0,1,...,n-1{p1,p2,...,pn}.
- Expansion (geometry)
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