What do you get when you go hunting for "a way to divide a cube equally in three-dimensional space? If you’re Naoki Yoshimoto and the year is 1971, you get the Yoshimoto Cube, a peculiar "polyhedral toy" that allows the transformation of a gold cube to a silver cube to a pair of gold and silver stars, then back. If you’re most of the rest of us, you get a neat toy and your noodle baked.
There’s a neat demonstration video up on YouTube, or you can see a line-art animation of the toy’s action at The World of Geometric Toy. Want one for yourself? MoMA sells them online, but be prepared to drop some coin…they’re about fifty bucks. That’s a fairly expensive form of pointless amusement, though a savvy mathematician could probably write it off as a business expense.