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We investigate the role of the Pauli Exclusion Principle (PEP) for light nuclei, at the examples of 12C and 16O. We show that ignoring the PEP does lead not only to a too dense spectrum at low energy but also to a wrong grouping into bands. Using a geometrical mapping, a triangular structure for 12C and a tetrahedral structure in 16O in the ground state is obtained by using the indistinguishably of the α-particles.