Still contemplating Dan's n-space regular simplices inscribed in a unit hypercube, the way one does, for n = 9 now. Given that for n = 7,8 the (conjectural) max side equals 2 , it was not a promising start that my rotation-jiggling search program took 12 hours to find just a couple of examples exceeding that: but the good-ish news is that for n = 9 a lower bound on the maximal side is 2.00452263 . Such configurations as warrent further investigation do not seem to have a great deal evident in the way of symmetry. More promising is their preponderance --- in one case two-thirds --- of coordinate components near --- within say 0.02 --- of an integer --- 0 or 1 --- which, one may assume, are on the way to eventually converge to interval endpoints. The freedom 1 + (n+1)n/2 similarity transforming current into limiting configuration is therefore by this stage well over-determined. If only there were an effective algorithm to compute it ... I ran up program which forces these near-endpoints to endpoints, in the process, destroying the regularity of the simplex, then attempts to restore regularity by minimising the side-length variance, with respect to individual cooordinate components iteratively. This works a treat on smaller cases already solved, but disappointingly fails to progress on the problem to hand. A less direct approach --- solving for the almost orthogonal projective matrix of the final transformation --- involves large numbers of simultaneous quadratic equations. This looks fairly horrible --- "quadratic programming", perhaps? Fred Lunnon