Truncation (InstanceTopic, 3)
From Hi.gher. Space
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:Truncates the polytope to its "midpoint". In odd dimensions, this is represented as the middle Coxeter-Dynkin node ringed. In even dimensions, the middle two nodes are ringed. | :Truncates the polytope to its "midpoint". In odd dimensions, this is represented as the middle Coxeter-Dynkin node ringed. In even dimensions, the middle two nodes are ringed. | ||
;Peritruncation | ;Peritruncation | ||
| - | :"Expands" the polytope. This is represented with the first and last nodes ringed. Etymology: [http://teamikaria.com/hddb/forum/viewtopic.php?p=17818#p17818 the Romanian for "outside" is "periferic"] - you can imagine the ringed nodes as being on the "outside" (at the ends) of the diagram. Interestingly, peritruncating a | + | :"Expands" the polytope. This is represented with the first and last nodes ringed. Etymology: [http://teamikaria.com/hddb/forum/viewtopic.php?p=17818#p17818 the Romanian for "outside" is "periferic"] - you can imagine the ringed nodes as being on the "outside" (at the ends) of the diagram. Interestingly, peritruncating a polyhedron or polychoron is equivalent to mesotruncating it twice, but it is not yet known whether this extends to higher dimensions. |
| + | ;Omnitruncation | ||
| + | :Gives the "largest", most "spherical" version of the root polytope, with the highest number of total elements. This is represented with all nodes ringed. Omnitruncating a polyhedron is equivalent to mesotruncating it and then 1-truncating the result, but it is not yet known whether this extends to higher dimensions. | ||
Revision as of 08:12, 5 February 2014
Truncation is the process of cutting polytope facets to produce new polytopes. The kind of truncation can be specified by a Dx number.
Particular types of truncation include:
- Mesotruncation
- Truncates the polytope to its "midpoint". In odd dimensions, this is represented as the middle Coxeter-Dynkin node ringed. In even dimensions, the middle two nodes are ringed.
- Peritruncation
- "Expands" the polytope. This is represented with the first and last nodes ringed. Etymology: the Romanian for "outside" is "periferic" - you can imagine the ringed nodes as being on the "outside" (at the ends) of the diagram. Interestingly, peritruncating a polyhedron or polychoron is equivalent to mesotruncating it twice, but it is not yet known whether this extends to higher dimensions.
- Omnitruncation
- Gives the "largest", most "spherical" version of the root polytope, with the highest number of total elements. This is represented with all nodes ringed. Omnitruncating a polyhedron is equivalent to mesotruncating it and then 1-truncating the result, but it is not yet known whether this extends to higher dimensions.
