My Pentagon Challenge is keeping  me busy. I am plowing my way through all of the pentagonal tiling types. Quite a few of them are built within either a perfect hexagon, or one that has been distorted beyond recognition. I am finding some interesting rules of symmetry I had not yet encountered. Wrapping my noggin around new concepts. Many of these symmetry types are skew-able, not only scale-able. Also, many of the anchor point for division lines inside hexagons are variable in their location, as long as the variable is kept constant for each pentagonal unit.I keep seeing these pentagons built using bungee cords on a pegboard. Variable lengths for the vectors, variable angles, variable locations for the anchor points. Some of the pentagonal symmetry types are built up of a single shape, one single unit repeats to create the surface, no gaps, no overlaps. Same symmetry rules as before: translation — rotation — reflection — glide. Some symmetry types are built using two, three, four, six different pentagons. No wonder it took so many people a great many years to figure all of it out.

I’ve repeated below, the images found on the wikipedia page about pentagonal tilings, but it is better to go to the page itself, as it shows the variables inside the rules, as an animation.

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Still much to learn. Keep you posted.