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In the concluding remarks of their 1993 published and now famous paper, JeffKahn and Gil Kalai wrote in particular: "Our construction shows that Borsuk'sconjecture is false for d = 1,325 and for every d > 2,014."  But, as Bernulf Weiszbach remarked in his paper from 2000, a simple (fewsteps for an upper-class pocket calculator) computation indicates that thatclaim is not true for d=1325.  William Kretschmer (Univ. of Texas) sent me his writeup on that paper by Kahnand Kalai, in particular pointing out that the derivation of the formula usedin that computation disregarded a certain aspect, that way missed the chance toremove one final halving from that formula and to indeed provide a proof that acertain point set is a counterexample for dimension 1325 (and all higherdimensions up to 1560, too).  This updated article takes a closer look at that derivation, gives an own,much more detailed and formal version of it that delivers theimproved/corrected formula, and contains some further conclusions.

On the counterexamples to Borsuk's conjecture by Kahn and Kalai