Partial Stott-expansion (no ontology)
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| - | '''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 | + | '''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 the previous construction is that this construction also used extended kaleido-facetings, a process discovered at the same time by student91. |
== Normal partiall Stott-expansion == | == Normal partiall Stott-expansion == | ||
Normal partial Stott-expansion works as follows: | Normal partial Stott-expansion works as follows: | ||
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octahedron: o2o || x2x || o2o | octahedron: o2o || x2x || o2o | ||
add x to the first node: x2o || u2x || x2o | add x to the first node: x2o || u2x || x2o | ||
| - | you now have | + | you now have an elongated square bipyramid, J15. |
== Partial Stott-expansion using extended kaleido-facetings == | == 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: | This works basically the same as normal expansion, with the additional step of taking some extended kaliedo-facetings. This thus gives the following: | ||
Revision as of 16:52, 27 August 2014
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 the previous construction is that this construction also used extended kaleido-facetings, a process discovered at the same time by student91.
Normal partiall 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.
