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We generalise a construction by Prokhorov & Reid of two families of   Q  ‐Fano 3‐folds of index 2 to obtain five more families of   Q  ‐Fano 3‐folds; four of index 2 and one of index 3. Two of the families constructed have the same Hilbert series and we study these cases in more detail.

Constructing Q ‐Fano 3‐folds à la Prokhorov & Reid