  Dyadic rationals are rationals whose denominator is a power of $2$. We define
dyadic $n$-dimensional convex sets as the intersections with $n$-dimensional
dyadic space of an $n$-dimensional real convex set. Such a dyadic convex set is
said to be a dyadic $n$-dimensional polytope if the real convex set is a
polytope whose vertices lie in the dyadic space. Dyadic convex sets are
described as subreducts (subalgebras of reducts) of certain faithful affine
spaces over the ring of dyadic numbers, or equivalently as commutative,
entropic and idempotent groupoids under the binary operation of arithmetic
mean.
  The paper contains two main results. First, it is proved that, while all
dyadic polytopes are finitely generated, only dyadic simplices are generated by
their vertices. This answers a question formulated in an earlier paper. Then, a
characterization of finitely generated subgroupoids of dyadic convex sets is
provided, and it is shown how to use the characterization to determine the
minimal number of generators of certain convex subsets of the dyadic plane.
