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We analyze the simple model of a rigid rotor with $C_{3}$ symmetry and showthat the use of parity simplifies considerably the calculation of itseigenvalues. We also consider a non-Hermitian space-time-symmetric counterpartthat exhibits real eigenvalues and determine the exceptional point at which theantiunitary symmetry is broken.

On a model for rotational tunneling with a $C_{6}$-space-time symetric analog