The modular structure of pyroxenes

The structures of pyroxenes can be described as cell-twins based on a common module (a layer) consisting of half the unit cell of the P2 (sub 1) /c polymorph. Atomic models of the different polymorphs are computed and the close similarity between the models and the corresponding experimental structures is shown. The cell-twin operations building the structures of pyroxenes are partial operations belonging to a special case of space groupoid which was called "twinned space group" in the pioneering studies by Ito started in 1935. The groupoid analysis of clino-, proto- and orthoenstatite is presented and the special place occupied by pyroxenes in the category of polytypes is discussed.