  We simplify a criterion (due to Ibarluc\'ia and the author) which
characterizes dynamical simplices, that is, sets $K$ of probability measures on
a Cantor space $X$ for which there exists a minimal homeomorphism of $X$ whose
set of invariant measures coincides with $K$. We then point out that this
criterion is related to Fra\"iss\'e theory, and use that connection to provide
a new proof of Downarowicz' theorem stating that any Choquet simplex is
affinely homeomorphic to a dynamical simplex. The construction enables us to
prove that there exist minimal homeomorphisms of a Cantor space which are
speedup equivalent but not orbit equivalent, answering a question of D. Ash.
