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The 17 Worlds of Planar Ants

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Classroom Adventures in Mathematics, Toronto, August 2014

Abstract. Back in early 2000, I got my first digital camera and set out to take pictures of my kids and of symmetric patterns in the plane. There are exactly 17 of those, no more, no less. It is an addicting challenge to walk around looking at buildings, brick walls, people's ties, fabrics, what's not, and to try figure out which of the 17 is each one.

What would history look like if we were living on Venus?
What do the ants on Lou Kauffman's tie think?
Which symmetry group appears twice in the pictures below?

cloud-covered planet Venus

Lou Kauffman

Lou Kauffman's tie