Moving to the hexagonal types, a TTTTTT tiling by definition has translated edges.
For both types a C edge must be paired with a G edge for the edges to translate so these pairs must be formed with center-point rotation. In the case of CG1CG2G1G2, the G1 edges are the edges that reflect over their midpoints. Because of symmetry, the translation block for both types is reduced to two.
In the beginning of this exercise I stated that I would use an asymmetric edge when possible. If an asymmetric edge is used for the TCCTGG type, the tile has no symmetry and the result is a translation block of four rather than the two in the above figure.