In article <firstname.lastname@example.org>, quasi <email@example.com> wrote:
>>There does not exist a PRUC pentagon.
>I'm now pretty sure the revised conjecture will also fail, and >while I don't have a counterexample, I do have a plan of action >that has a reasonable chance of finding such a counterexample. >When I get a chance, unless someone else finds a counterexample >first, I'll try to implement the plan.
Have you got anywhere with this? I have searched up to radius 500 and found none. All the rational pentagons I found have a rational diagonal, and almost all have a diameter as a diagonal. A few have *all* the diagonals rational, so you could inscribe a rational pentagram in a rational pentagon, e.g. 65: 32 50 66 78 126.