  We provide a simple characterization of simplicial complexes on few vertices
that embed into the $d$-sphere. Namely, a simplicial complex on $d+3$ vertices
embeds into the $d$-sphere if and only if its non-faces do not form an
intersecting family. As immediate consequences, we recover the classical van
Kampen--Flores theorem and provide a topological extension of the Erd\H
os--Ko--Rado theorem. By analogy with F\'ary's theorem for planar graphs, we
show in addition that such complexes satisfy the rigidity property that
continuous and linear embeddability are equivalent.
