Teruhisa Sugimoto has a draft paper that enumerates 17 types of convex, finitely surroundable pentagons! I hope to be able to read an English translation at some point. tilingpackingcovering.web.fc2.

And finally, the dramatic conclusion to my series on Heesch numbers: does there exist a convex pentagon that can be surrounded, but doesn't tile the plane, and admits a surround that's edge-to-edge? Heesch's original 1968 shape does all of the above except the edge-to-edge part. isohedral.ca/heesch-numbers-pa mathstodon.xyz/media/a0bUlDZY_

The story of Heesch numbers continues in two posts. In isohedral.ca/heesch-numbers-pa, I compute Heesch numbers of polyominoes and polyiamonds in search of interesting new examples; in isohedral.ca/heesch-numbers-pa, I present a new family of simple polygons, all with Heesch number 1.

Time to justify my presence here...

The Heesch number of a shape is the maximum number of layers of copies of that shape by which you can surround it. Heesch's Problem asks which positive integers can be Heesch numbers. I'll show a few fun new results over a series of blog posts; today, I offer a basic introduction to the topic. isohedral.ca/heesch-numbers-pa


Mathematical news doesn't usually make me squee, but I'm positively delighted that Cédric Villani was elected to the French parliament.

Happy to join my mathematical friends on this instance. I'll try to find an excuse to say interesting things.


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