Math Monday: Egg carton constructions

By George Hart for the Museum of Mathematics

Save your egg cartons and see what recycled art you can make with them! You can cut the bottoms of egg cartons into strips of six “waffle holes” which then interlock, without glue, into interesting structures. The basic joint of four spiraling strips is seen below. The end of each locks under the adjacent waffle hole of the next, always keeping a consistent handedness. This cuboctahedron is made from a dozen cartons. A gross of eggs provided the sustenance for me to arrange the twenty-four strips so that at each joint, in cyclic order, the openings are of the form: square, triangle, square, triangle.

This method of construction is the idea of Jeannine Mosely, who displayed models at the OrigamiUSA conference. You can work up to complex structures by first making a simple octahedron from twelve strips. There are four triangular openings at each vertex:

Here is how the octahedron lays out flat before curving and interlocking the strips:

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