Fit two identical 90-degrees cones base to base, slice the resulting shape in half vertically, and give one of the halves a quarter turn. The result is a sphericon, a solid that rolls with a bemusing meander: Where the original double cone rolls only in circles, the sphericon puts first one conical sector and then the other in contact with a flat surface beneath it, giving it a smooth but undulating trajectory sustained by a fixed center of mass.
And that’s just the start. “Two sphericons placed next to each other can roll on each other’s surfaces,” writes David Darling in The Universal Book of Mathematics. “Four sphericons arranged in a square block can all roll around one another simultaneously. And eight sphericons can fit on the surface of one sphericon so that any one of the outer solids can roll on the surface of the central one.” See the video for more.