low degree), can limit the number of allowed structural phases for the system in its ground state.

Parametrization of strata in orbit spaces of compact linear groups
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Let $G$ be a compact linear group, acting orthogonally in $\real^n$ and $\{p\}$ be a related MIB. We shall prove that the possibility of parametrizing the principal stratum of the orbit space of a coregular group in terms of parameters related to the elements of a MIB can be extended to singular strata. The result stems from the proof of the following statement: [*the set of interior points of the topological closure of an isotropy–type stratum, with orbit–type $(H)$, is diffeomorphic to the principal stratum of the orbit space of a group space of the stabilizer of $H$ in $G$.*]{} If the stabilizer turns out to be coregular, the constructive proof of this proposition will provide a one-to-one rational parametrization of the stratum. Since, in view of possible applications, we are mainly interested in the possibility of getting a one-to-one parametrization of a stratum, in the presentation of our results, stress will be laid on this aspect of the matter.

Let $H$ be a proper isotropy subgroup of the $G$-space $(G,\real^n)$. We 