Pentagonal tiling #tessellations, Part 2

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. Continue reading

Pentagonal tiling #tessellations, Part 1

Another challenge showing up on my desk, compliments of Woodpecker Carving. Hussein posted a beautiful Islamic geometric design, displaying the use of pentagons. But wait I thought, aren’t pentagons impossible to tile using the original seventeen symmetry groups? Or so I thought. I had seen intriguing examples of pentagonal tiles over the years, but I was still obsessed with M.C. Escher type nested shapes – and will always be. Continue reading

Symmetricks / Symétrucs & Tessellations

All this talk about sharing space between characters in a tessellation has made me think of the word “symétruc”, which I coined a few years ago in a discussion with Jeff Weeks, American mathematician and KaleidoPaint app programmer. My original intention was for a word better than the French “pavages”, or “dallages”, which to me aludes to floor tiles, patio stones or asphalt pavement, rather than graphic art. Tessellation can be used in French, I’ve since found out.  Continue reading