  Motivated by some questions in Euclidean Ramsey theory, our aim in this note
is to show that there exists a cyclic quadrilateral that does not embed into
any transitive set (in any dimension). We show that in fact this holds for
almost all cyclic quadrilaterals, and we also give explicit examples of such
cyclic quadrilaterals. These are the first explicit examples of spherical sets
that do not embed into transitive sets.
