Truncation (InstanceTopic, 3)
From Hi.gher. Space
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. Keiji had previously erroneously called this "rectification", however they are only the same in 3D: true rectification is represented with only the second node ringed, regardless of dimension.
- 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.