This work deals with the crystal-structure deduction of new structural types of Bi3+-M2+ oxyphosphates (M is a transition element) from HREM images. Previous studies showed the unequivocal attribution of particular HREM contrasts to the corresponding Bi/M/O-based polycationic species in similar materials. On this basis, the examination of isolated crystallites of polyphased samples led to new HREM contrasts assigned to new polycationic species in three new structural types. This helped us to solve one crystal structure, and the two other forms have been deduced through HREM image decoding. It helped to model the investigated materials from the structural point of view as well as the chemical one. The three assumed crystal structures are formed by polycationic ribbons, n tetrahedra wide, surrounded by PO4 groups, as already encountered in these series of oxyphosphates. However, here we deal with the original n = 4-6 cases, whereas, up to this work, only the n = 1-3 ribbons have been reported. The greater size of ribbons is associated with particular structural modifications responsible for complex HREM contrasts. The validity of the proposed models is verified in Part 2 of this work.