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Topological and geometrical methods are used to calculate thepseudorotational part of the vibronic spectrum for an electronic triplet of anoctahedral, tetrahedral, or icosahedral molecule. The calculations take intoaccount the nontrivial geometry inherent in the Jahn-Teller effect. It is shownthat the Jahn-Teller effect gives rise to a geometry, which is related to theisoparametric geometry of E. Cartan. The pseudorotational spectra correspond tothe spectra of connection Laplacians on nontrivial line bundles over basespaces with this geometry. Globally, the isoparametric submanifolds form atotally geodesic foliation of S^4 and the spectral flow of these connectionLaplacians on this foliation is computed.

Pseudorotations in Molecules: Electronic Orbital Triplets