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A supersymmetric extension of the dynamical symmetry group $Sp^{B}(12,R)$ ofthe Interacting Vector Boson Model (IVBM), to the orthosymplectic group$OSp(2\Omega/12,R)$ is developed in order to incorporate fermion degrees offreedom into the nuclear dynamics and to encompass the treatment of odd massnuclei. The bosonic sector of the supergroup is used to describe the complexcollective spectra of the neighboring even-even nuclei and is considered as acore structure of the odd nucleus. The fermionic sector is represented by thefermion spin group $SO^{F}(2\Omega)\supset SU^{F}(2)$.  The so obtained, new exactly solvable limiting case is applied for thedescription of the nuclear collective spectra of odd mass nuclei. Thetheoretical predictions for different collective bands in three odd massnuclei, namely $^{157}Gd$, $^{173}Yb$ and $^{163}Dy$ from rare earth region arecompared with the experiment. The $B(E2)$ transition probabilities for the$^{157}Gd$ and $^{163}Dy$ between the states of the ground band are alsostudied. The important role of the symplectic structure of the model for theproper reproduction of the $B(E2)$ behavior is revealed. The obtained resultsreveal the applicability of the models extension.

Collective states of the odd-mass nuclei within the framework of the Interacting Vector Boson Model