The Beckman-Quarles theorem for rational d-spaces, d even and d≥6

Let V d denote the set {A 1,B 1,A 2,B 2,…,A d ,B d } in Q d . The polytope Pd=conv(V d ) is,

of course, a cross-polytope in Q d . The set V d is a two-distances set,

1 This paper was written while J.Zaks was visiting R.Connelly at Cornell University. The Zaks wish to express their gratitude to Gail Dennis and Bob Connelly for their superb hospitality.