  We give a new, simple, dimension-independent definition of the serendipity
finite element family. The shape functions are the span of all monomials which
are linear in at least s-r of the variables where s is the degree of the
monomial or, equivalently, whose superlinear degree (total degree with respect
to variables entering at least quadratically) is at most r. The degrees of
freedom are given by moments of degree at most r-2d on each face of dimension
d. We establish unisolvence and a geometric decomposition of the space.
