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. I have finally found a bit of time to start a study and hopefully an understanding of pentagonal tiling. I think it will be a long time to completion. Like a few years! Hey, I like a challenge.

Another spur in the past few months about pentagons, was an obituary notice for Marjorie Rice, a tessellation artist from the States. She was part of the extensive list of people involved in the study of pentagonal tiling, in the past century. An article in Quanta Magazine explains the pentagon dilemma quite well.

A dozen or so contributors took about 100 years to figure it all out, and confirm it all using computers.

This Wikipedia article “Pentagonal Tiling” is a little more complex than the Quanta magazine exploring the dilemma with pentagons, and the place I go to understand my next challenge.

Below are my first dozen tessellations exploring the regular division of the plane using convex pentagons. In some instances the patterns are monohedral (using only one tile throughout) sometimes 2 different pentagons, sometimes three. I have yet to understand the complexity of this task, as well as the jargon. Should be fun.

 

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