28 Nov
2006
28 Nov
'06
11:52 a.m.
On 11/28/06, Michael Kleber <michael.kleber@gmail.com> wrote:
This looks like fun; wish I'd had the time to play with it.
Starting with a 3-4-5 triangle, for example, and clearing denominators at the end, Bill's geometric construction yeilds the hexad
108, 144, 180, 5*sqrt(373), 13*sqrt(229), sqrt(44749)
which I'm sure Fred's program will agree has three volume-zero tetrahedra and no degeneracy.
Yup, it checks out [blowing me out of the water once more] --- three distinct planar charts, besides one triple and three double proper tetrahedra [distinct shapes, equal volumes]. My dismal prognosis for finding an integer hexad turns out to result from an ingeniously gross program bug. BTTDB again, WFL