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We generalise an argument of Leader, Russell, and Walters to show that almost all sets of    d  +  2    points on the    (  d  ‐  1  )   ‐sphereS    d  ‐  1are not contained in a transitive set in someR   n   .

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