Collective rotation of tetrahedral nuclei is analyzed within a three-dimensional cranking model. The favored orientation of the rotational frequency vector with respect to the turning nucleus as function of angular momentum is obtained from the total energy calculations. A new quantum number, resulting from the particular symmetry of the cranking Hamiltonian of the nuclei with tetrahedral nuclei is discussed. Some consequences for the structure of the rotational bands are presented.

PACS numbers: 21.10.-k, 21.60.-n, 21.60.Fw