  We investigate orthogonal representations of compact Lie groups from the
point of view of their quotient spaces, considered as metric spaces. We study
metric spaces which are simultaneously quotients of different representations
and investigate properties of the corresponding representations. We obtain some
structural results and apply them to study irreducible representations of small
copolarity. As an important tool, we classify all irreducible representations
of connected groups with cohomogeneity four or five.
