We construct 16 reflection groups Γ acting on symmetric domains $\mathcal {D}$ of Cartan type IV, for which the graded algebras modular forms are freely generated by same weight, and in particular Satake-Baily-Borel compactification {D}/ {\Gamma }$ is isomorphic to a projective space. Four these previously known results Freitag-Salvati Manni, Matsumoto, Perna Runge. In addition we find several ...