Recently, I came up with a family of patterns which result from placing four modified twists around the corners of a rectangle or square. Some variations are flagstone tessellations, others “almost flagstone” tessellations and through modifications, one can arrive at a number of other interesting patterns. Since the family is large and very interesting, it will take me some time until I can neatly fold a reasonable number of models. I will try to post them “in logical order” to show how one leads to the other, which is a different order than I actually fold the models. Obviously, a clean fold takes much more time than an ugly proof-of-concept model.
At least some of these models have been known for a long time. The Pythagorean Tiling aka Two Square Tessellation which was the starting point of my journey, has independently been designed before me by Alex Bateman and Peter Keller. Quite possibly, by others as well. Recently, Madonna Yoder posted a number of folds which belong to the same family.
This box is decorated with a molecule of one of the pseudo-flagstone patterns which belong to the above-mentioned family of tessellatons.