A probably maximal 8-space regular simplex inscribed in the unit hypercube, with side = 2 and vertices [ a, 0, a, 0, a, 0, a, 0 ], [ 1, 1, 1, 1, 1, 1, 0, 0 ], [ 0, 1, 0, 1, 1, 0, 0, 1 ], [ 1, 1, 1, 1, 0, 0, 1, 1 ], [ 0, 1, 1, 0, 0, 1, 0, 1 ], [ 1, 1, 0, 0, 1, 1, 1, 1 ], [ 1, 0, 0, 1, 0, 1, 0, 1 ], [ 0, 0, 1, 1, 1, 1, 1, 1 ], [ 0, 1, 0, 1, 0, 1, 1, 0 ], where (as is customary) a := 1/2 ; symmetry is 4-cyclic. Two things I a find difficult to credit about this result: the first is that my spatchcock algorithm is still capable of producing any result at all; the second is that Warren has yet again opined what appears surely to be a sharply maximal result, on the grounds of what he admits was a goofball reason ... Updated <dim, side, content> table: <0, 1.000000000000000, 1.000000000000000>, <1, 1.000000000000000, 1.000000000000000>, <2, 1.035276180410083, 0.4641016151377546>, <3, 1.414213562373095, 0.3333333333333333>, <4, 1.414213562373095, 0.09316949906249124>, <5, 1.511173070871356, 0.02843743486232121>, <6, 1.581138830084190, 0.007177059763087539>, <7, 2.000000000000000, 0.006349206349206349>, <8, 2.000000000000000, 0.001190476190476190>; (technically, lower bounds on maxima achievable). Speechless! Fred Lunnon