Math factoid of the day: 59 icosahedra

I’ve long been fascinated by stellation, the process of extending a polyhedron’s faces to form new structures. The word stellation is from the Latin root for star, so it means to make star-like. The star that graces the upper-left corner of this site is a stellated dodecahedron.To understand stellations, let’s start with two dimensions. Consider a regular pentagon. If we extend the sides of the pentagon, they will intersect again, making a five-pointed star:(image from brilliant.org.)Looked at...

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