The van Kampen-Flores theorem states that the n-skeleton of a
(2n+2)-simplex does not embed into R2n. We give two proofs for
its generalization to a continuous map from a skeleton of a certain regular CW
complex (e.g. a simplicial sphere) into a Euclidean space. We will also
generalize Frick and Harrison's result on the chirality of embeddings of the
n-skeleton of a (2n+2)-simplex into R2n+1.Comment: 10 pages, some of the results (especially Theorem 1.4 and Corollary
1.5) were improved, final version, to appear in Discrete & Computational
Geometr