On 12/19/06, James Buddenhagen <jbuddenh@gmail.com> wrote:
This raises the question of whether there are conspheric ones with no tetrahedral cells planar or other degeneracies. Presumably there are, so what is the 'smallest' one?
In 2-space, I found 250 disitnct proper integer charts with max sum of edge lengths 111, most of which belong to the special 4-parameter (concyclic) trapezium family mentioned earlier. Excluding these there remain just 53, including 19 concyclic: so approximately one third of the non-trapezoidal total is concyclic. In 3-space, I have now searched up to edge-length 8, finding 26 proper integer charts --- list available on request. None is conspheric, and none has an edge of length unity. Draw your own conclusions! Fred Lunnon