This is a systematic distortion of polytopes by contraction and dilation of the edges. The systen is very good for small dimensions, where there is not a lot of things to do, and lots of things to do it on.
The notation consists of adding a modifier prefix to the polytope being modified. For example, tt{3,3,5} is a truncate tetrahedron. It is often applied to the Schlafli Symbol.
In three dimensions, there are three degrees of freedom, and three edges, so the class regularly forms with equal edges.
In four dimensions, there are four degrees of freedom, and six edges. This rarely forms a figure with all edges equal.
The ss{3,4,3} is actually derived from alternate verticies of a truncated {3,4,3}, not an omnitruncated one. It may be derived by removing 24 verticies of an inscribed {3,4,3} from a {3,3,5}. This replaces clusters of 20 tetrahedra with an icosahedron.
The ss{3,3,5} is derived from the {3,3,5} by removing just two of its girthing decagons: two that are furtherest apart. Each vertex would had been replaced by an icosahedron, but each of these loose a polar region, leaving just a pentagonal antiprism.
The notation has a large number of parallel irregular terms. While this cuts the number of different figures down by paired constructions, the constructions themselves are not further analised.
None the less, this notation does not rely heavily on assorted assumptions about symmetry groups, and is fairly general. The notion of "define and extend" makes it useful for exploring and classifying new polygopes.
Copyright 2002 Wendy Krieger