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- Omnitruncation abstract "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 File:CDel node 1.pngFile:CDel p.pngFile:CDel node 1.png 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: File:CDel node 1.pngFile:CDel p.pngFile:CDel node 1.pngFile:CDel q.pngFile:CDel node 1.png For uniform polychora (4-polytopes): A runcicantitruncation (great prismation), t0,1,2,3{p,q,r}. (Application of runcination, cantellation, and truncation operations) Coxeter-Dynkin diagram: File:CDel node 1.pngFile:CDel p.pngFile:CDel node 1.pngFile:CDel q.pngFile:CDel node 1.pngFile:CDel r.pngFile:CDel node 1.png, File:CDel nodes 11.pngFile:CDel split2.pngFile:CDel node 1.pngFile:CDel p.pngFile:CDel node 1.png, File:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes 11.pngFile:CDel split2.pngFile:CDel node 1.png 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: File:CDel node 1.pngFile:CDel p.pngFile:CDel node 1.pngFile:CDel q.pngFile:CDel node 1.pngFile:CDel r.pngFile:CDel node 1.pngFile:CDel s.pngFile:CDel node 1.png, File:CDel nodes 11.pngFile:CDel split2.pngFile:CDel node 1.pngFile:CDel p.pngFile:CDel node 1.pngFile:CDel q.pngFile:CDel node 1.png, File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes 11.pngFile:CDel split2.pngFile:CDel node 1.png For uniform n-polytopes: t0,1,...,n-1{p1,p2,...,pn}.".
- Omnitruncation wikiPageID "7083690".
- Omnitruncation wikiPageRevisionID "603809300".
- Omnitruncation anchor "Truncation".
- Omnitruncation hasPhotoCollection Omnitruncation.
- Omnitruncation title "Expansion".
- Omnitruncation title "Truncation".
- Omnitruncation urlname "Expansion".
- Omnitruncation subject Category:Polyhedra.
- Omnitruncation subject Category:Uniform_polyhedra.
- Omnitruncation comment "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}.".
- Omnitruncation label "Omnitruncation".
- Omnitruncation sameAs m.0h3cgh.
- Omnitruncation sameAs Q7090413.
- Omnitruncation sameAs Q7090413.
- Omnitruncation wasDerivedFrom Omnitruncation?oldid=603809300.
- Omnitruncation isPrimaryTopicOf Omnitruncation.