Weber has proved that if 2m 3(n + 1) then an n-dimensional polyhedron K embeds in R m if and only if there exists an equivariant map from the deleted product K * into the sphere S m - 1 . As a consequence he has obtained that in the same range of dimensions an n-dimensional polyhedron embeds in R m if and only if it quasi embeds in R m . We show that for m max(4, n) the dimension restrictions in Weber's results are necessary in all cases. This leaves only two open cases remaining (namely m = 3 and n = 2 or 3) in related questions about embeddings.