ALMOST ALL SETS OF $d+ 2$ POINTS ON THE $(d- 1)$-SPHERE ARE NOT SUBTRANSITIVE.

We generalise an argument of Leader, Russell, and Walters to show that almost all sets of $d+ 2$ points on the $(d- 1)$-sphere ${S}^{d- 1} $ are not contained in a transitive set in some ${\mathbf{R} }^{n} $. [ABSTRACT FROM PUBLISHER]