Symmetry Group P1 is the most simple of all symmetry systems. A repeat or translation, of your design both vertically and horizontally. That’s it!
The shape is up to you as long as it repeats in those two directions, and is built around a four sided figure, square, rectangle, or skewed into a lozenge. No mirrors, no rotations, no glides — simply a translation. Similar to a stamp, you can usually locate the four corners of the unit cell, with just a bit of observation of the design. Something I used to do as a kid, looking at something till I found the repeating area. Some of these designs can take a while to dissect, like the Camo, or the Village tessellations. The edges are well hidden. Some are quite easy, like Fish Bones or Ocean Spray Surf.
This post will be the first in a series of 17, as there are 17 symmetry groups that tile the two dimensional surface, aka, the plane.