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What is a polydude?
editWhen this page was created, it listed the enumeration of n-dudes for values of n from 1 to 6. But what is a polydude? The Mathpuzzle page by Ed Pegg Jr. says it is a polydrafter that does not "have any 30 degree vertices, or weakly hanging triangles." This is not two different ways of saying the same thing. Some polydrafters have 30° corners and no weakly hanging triangles.
What does "weakly hanging" mean? It could mean attached only by the short leg. It could also apply to a cell attached only by half its hypotenuse, to the short leg of another cell. And extended polydrafters have other possibilities, though Pegg does not consider extended polydrafters.
Pegg enumerates polydudes up thru 12 cells. I suspect that it was Miroslav Vicher who enumerated them. One of Vicher's pages [1] shows constructions with what Pegg calls "the 15 pentadudes" and "the 59 hexadudes." After looking at Vicher's set of pentadudes, I see no simple rule for characterizing them.
Entry A056843 in the Online Encyclopedia of Integer Sequences includes a note by David R. Wasserman. Wasserman says in effect that the precise definition of polydude is not known, and offers an ingenious conjecture that he says does not quite fit Vicher's enumeration. Sicherman (talk) 01:43, 8 May 2018 (UTC)
- Sources for the term polydude seem very sparse. Maybe we should just remove it? Alternatively, if we could find published sources for the ambiguity of definition, we could say that it's ambiguous. —David Eppstein (talk) 05:37, 8 May 2018 (UTC)
- So long as some combinatorial geometers are using the term polydude, I think that Wikipedia should go on mentioning it. Later the geometers may clear up the uncertainty. Then we can clear up the definition on this page. Sicherman (talk) 22:53, 4 August 2020 (UTC)