New topological models for Banach-Mazur compacta

Sufficient conditions are given for an action of the orthogonal group O(n) on the Hilbert cube Q in order that the corresponding orbit space Q/O(n) be homeomorphic to the Banach-Mazur compactum BM(n). This result is applied to obtain simple topological models for BM(2). __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 19–31, 2005.