Polya's 17 plane filling illustrations
In 1924 George Polya recorded 17 illustrations in a journal article that would describe each symmetry group. I copied them down and I hope to use these for my own purposes sometime in the future.I find these fascinating because I've enjoyed this type of organization all my life but I've never been able to. my favorite is D3°, the arrangement colored purple green and orange on the fourth page, It feels very regal. Like I would most see it in a palace or a cathedral.
theoretically, each of these could continue forever. In addition to that, you could create your own repeating illustrations by following certain rules including: 1) The new figure must have the exactly same area equal to the original shape and 2) Its outline must be shaped so that when it cuts through one of the corners or midpoints of a shape, a rotation of 180° about that point would turn it into an adjacent copy of itself.
In order to fulfill this requirement, portions of the boundary of such a figure must have a center of symmetry, such as that found in the letters S, N, or Z.







































