Partial Stott-expansion (no ontology)

From Hi.gher. Space

Partial Stott-expansion is Stott-expansion where you are using a lower symmetry than the full symmetry of the polytope. The process using this definition has been discovered in 2013 by Klitzing. In 2014 Quickfur found a way to construct a bilbiro from an icosahedron. This construction turned out to be a partial Stott-expansion as well. The difference with Klitzings partial expansions that this construction also used extended kaleido-facetings, a process discovered at the same time by student91.

Normal partial Stott-expansion

Normal partial Stott-expansion works as follows: first, take the representation of a polytope that uses dynkin-symbols. Then, add an x to all nodes of one kind.

Example: octahedron: o2o || x2x || o2o add x to the first node: x2o || u2x || x2o you now have an elongated square bipyramid, J15.

Partial Stott-expansion using extended kaleido-facetings

This works basically the same as normal expansion, with the additional step of taking some extended kaliedo-facetings. This thus gives the following: first, take the representation of a polytope that uses dynkin-symbols again. Then, you apply the kaleido-facetings to some parts of the reresentation. finally, you add x to all nodes of one kind again.

Example: icosahedron: o2x || f2o || x2f || f2o || o2x Do some extended kaleido-facetings: o2(-x) || f2o || x2f || f2o || o2(-x) add x to the second node: o2o || f2x || x2F || f2x || o2o you now have a bilunabirotunda, J91.