Math Monday: Polyhedral Pop

by Glen Whitney for the National Museum of Mathematics

From the bins at the 99 cent store to the displays at funky boutiques in Venice, CA, polyhedra are having their fifteen minutes of fame.

Taylor, Riley, Jordan, and Shay are redecorating the apartment they share. One evening, after a day of shopping, they all gather in the living room to show off their respective finds. Riley pipes up first. “Everyone is always dropping jackets on the floor in the front hall. So I got these shiny icosahedral coat hooks we can put up.” 20161228_134100 “That’s cool,” responds Shay, “I felt like nobody can ever find a pen in here, so I got these stylish antiprismatic pen holders for us to share. Which one’s your favorite polygon?” 20161125_164658 Taylor breaks in, “Wow! I thought this place needed more plants, so I got these two glass planters — one is a compound of an octagonal pyramid and frustum, and the other is an unusual polyhedron that illustrates Euler’s theorem on pentagon-hexagon polyhedra.”
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Jordan puts it all together: “Are you guys kidding? Did we all end up with polyhedra? I mean, I just stopped in for some snacks, and couldn’t resist this rhombicuboctahedron. 20161230_201811 What other polyhedra did you guys find?”

“Well,” admits Riley, “for decoration I thought these shapes might be cool: elevated Archimedean solids and seven-pointed stars.”
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“And I thought it would be fun to play with these irregular polyhedral blocks with the interesting property that every pair of opposite faces is parallel, so they can always stack straight.” offers Shay.
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Taylor adds, “At the 99 cent store, I got these construction sets that make some pretty esoteric polyhedra, for when my nieces and nephews visit.”
“I even saw just a picture of a polyhedron on sale as home decor (although I’m not quite sure if the shape pictured can actually be built),” concludes Jordan. “Isn’t it amazing how ubiquitous these kinds of shapes have suddenly become?”
If you spy any intriguing polyhedral products to be added to Taylor, Riley, Jordan, and Shay’s list, tell us about them at

PS about the snowflake program mentioned in a recent column: the Evil Mad Scientist points out that it already anticipated our suggestion to be able to change the symmetry as you go; you can read all about it in this blog entry. Thank you, Evil Mad Scientist!