Snowflakes. They’re beautiful to look at and taste good, too, and who doesn’t like an excuse to skip class on a blustery January morning? Surely, though, snowflakes are more than that, aren’t they?

YouTube vlogger Vi Hart shows viewers how to construct realistic paper snowflakes in a video titled “Snowflakes, Starflakes, and Swirlflakes.”  Hart takes a piece of paper, folds it in half twice, and then folds it in thirds before cutting out any number of designs she can think of. After reading this, you might as well practice making snowflakes with this very paper – not  only is it a great way to fill your suddenly wide-open schedule, it’s a fun way to recycle, too.

But why stop at arts and crafts when we can dive deeper into science – and what kind of science? The purest of them all: Mathematics.

Imagine a “regular” polygon with sides of equal length – such as the hexagon you can impose over most snowflakes. Any motion (such as a rotation or a reflection) that leaves this polygon unchanged, or “invariant,” belongs to a dihedral set. Hexagons (and therefore snowflakes) belong to the dihedral set D₆, which contains 12 possible motions. Why not try to figure them all out?

Even more amazing is the fractal nature of snowflakes. Fractals are structures that are self-symmetric – that is, when you “zoom in” on the picture, it looks like the picture was unchanged. One famous fractal, called the Koch Snowflake, is formed by drawing a six-sided star, replacing the center third of each straight line segment with two sides of an equilateral triangle, and then repeating the process to infinity. With each succession, the curve becomes fuzzier and fuzzier, much like the blanket you’ll probably be wrapped up in all weekend.