  We show that infinitely many Gorenstein weakly-exceptional quotient
singularities exist in all dimensions, we prove a weak-exceptionality criterion
for five-dimensional quotient singularities, and we find a sufficient condition
for being weakly-exceptional for six-dimensional quotient singularities. The
proof is naturally linked to various classical geometrical constructions
related to subvarieties of small degree in projective spaces, in particular
Bordiga surfaces and Bordiga threefolds.
