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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
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* For regular polygons: An ordinary truncation, t0,1 = t = .
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* Coxeter-Dynkin diagram
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* For uniform polyhedra (3-polytopes): A cantitruncation (great rhombation), t0,1,2 = tr. (Application of both cantellation and truncation operations)
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* Coxeter-Dynkin diagram:
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* For Uniform 4-polytopes: A runcicantitruncation (great prismation), t0,1,2,3. (Application of runcination, cantellation, and truncation operations)
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* Coxeter-Dynkin diagram: , ,
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* For uniform polytera (5-polytopes): A steriruncicantitruncation (great cellation), t0,1,2,3,4. (Application of sterication, runcination, cantellation, and truncation operations)
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* Coxeter-Dynkin diagram: , ,
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* For uniform n-polytopes: t0,1,...,n-1.
== See also ==
* Expansion (geometry)
* Omnitruncated polyhedron
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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