A class of higher-spin gauge theories on AdS4 associated with various Coxeter groups \( \mathcal{C} \) is analyzed at the linear order. For a general \( \mathcal{C} \) , a solution corresponding to the AdS4 space and the form of the free unfolded equations are established. A disentanglement criterion has been formulated for Coxeter HS modules. The shifted homotopy technique is uplifted to the general Coxeter HS models. In case of the Coxeter group B2 classification of unitary HS modules and a consistent truncation to them are determined, the dynamical content is discussed briefly.
