On 1/5/07, Fred lunnon <fred.lunnon@gmail.com> wrote:
I wonder if the second one in particular is a member of a parametric family, analogous to the quadratic 4-parameter trapezium family in 2 dimensions?
Despite appearances, there are in practice rather a lot of 5-vertex 3-dim cases which satisfy MK's "isosceles" constraint --- say AD = AE, BD = BE, CD = CE: 21 of the first 63 may be cast in this form; and 12 of those have sufficient symmetry to do so in two distinct ways. However, staring hard at these 33 cases soon dispels any hope for a simple parametric formula; and the impression is reinforced by an attempt to construct one via algebraic geometry, resulting in a quartic irrational parameterisation. Fred Lunnon PS --- after laboriously transcribing between MK ordering and WFL ordering, I belatedly realised that all that was required was to reverse the vector ...