Facetings of a polyhedron
Posted: Sun May 01, 2022 4:24 pm
Hi Rob,
Long time no see. Off and on I have been working on the underlying theory of polytopes, with a view to applying it to stellations and facetings. Now that I have at last got there, I am interested in enumerating the facetings of the regular dodecahedon in particular. (I published its faceting diagram along with several others a good many years ago, in the Mathematical Gazette).
Your current info on Great Stella says that users can step through the allowed facetings, according to the rules selected. Are these just the rules for the dual stellations, or have you developed a set of rules directly applicable to facetings? Is there such a thing as a count of the permitted facetings, other than the count of the permitted stellation cell sets? This is particularly relevant, as some distinct facetings yield the identical cell set for the dual stellation.
Long time no see. Off and on I have been working on the underlying theory of polytopes, with a view to applying it to stellations and facetings. Now that I have at last got there, I am interested in enumerating the facetings of the regular dodecahedon in particular. (I published its faceting diagram along with several others a good many years ago, in the Mathematical Gazette).
Your current info on Great Stella says that users can step through the allowed facetings, according to the rules selected. Are these just the rules for the dual stellations, or have you developed a set of rules directly applicable to facetings? Is there such a thing as a count of the permitted facetings, other than the count of the permitted stellation cell sets? This is particularly relevant, as some distinct facetings yield the identical cell set for the dual stellation.