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We prove the validity of the freeness conjecture of Brou\'e, Malle andRouquier for the generic Hecke algebras associated to the exceptional complexreflection groups of rank 2 belonging to the tetrahedral and octahedralfamilies, and we give a description of the basis similar to the classical caseof the finite Coxeter groups.

The BMR freeness conjecture for the tetrahedral and octahedral families