Put two points on the same side of a blue parallelogram, then put third point on an adjoining paral. Congratulations, you've just made a p1 tiling pattern. Other 16 groups are coming soon.

oblique (p1, p2)
rectangular (pm, pg, p2mm, p2mg, p2gg)
centered rectangular (cm, c2mm)
square (p4, p4mm, p4gm)
hexagonal (p3, p3m1, p31m, p6, p6mm)