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In geometry, an omnitruncation is an opera … 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, .
* Coxeter-Dynkin diagram
* For uniform polyhedra (3-polytopes): A cantitruncation, . (Application of both cantellation and truncation operations)
* Coxeter-Dynkin diagram:
* For uniform polychora: A runcicantitruncation, . (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}. . (Application of sterication, runcination, cantellation, and truncation operations)
* Coxeter-Dynkin diagram: , ,
* For uniform n-polytopes: .diagram: , ,
* For uniform n-polytopes: .
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