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
A list of M.C. Escher show around the globe, for this year and years past.
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
This one is going to take quite some time to complete. Stay tuned! It started off as an exercise in tessellating pentagons. Not an easy task. It took mathematicians over a 100 years to figure out all of the ways it could be accomplished. Good article about pentagons on the Quanta Magazine website, check it out. Continue reading
I was approached by a student a few months ago — he was writing his dissertation and needed examples to illustrate the seventeen symmetry groups: Continue reading
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
On the theme of ‘multiple sharing’ (as with ‘Mountain Biker’), are you familiar with the work of Raoul Raba in Zoo Mathématique? He has occasional examples. As a concept, there are not too many artists using this idea in their tessellation work. The premise of ‘economy’ is a pleasing one. Continue reading