In what follows tilings that have a translation block of one are presented when possible. If asymmetric edges are possible, they are used, then edges with reflective symmetry over their midpoints, with edges formed using center-point rotation only as a last resort.
First, a TTTT type.
Type C3C3C6C6 cannot be formed with translated edges because the template cannot be a parallelogram.
Part four will continue with hexagonal types.