  We study the sets DF({\beta}) of digit frequencies of {\beta}-expansions of
numbers in [0,1]. We show that DF({\beta}) is a compact convex set with
countably many extreme points which varies continuously with {\beta}; that
there is a full measure collection of non-trivial closed intervals on each of
which DF({\beta}) mode locks to a constant polytope with rational vertices; and
that the generic digit frequency set has infinitely many extreme points,
accumulating on a single non-rational extreme point whose components are
rationally independent.
