The Yoshimoto Cube
The Yoshimoto cube was invented by the Japanese designer Naoki Yoshimoto in 1971. The cube is made up of eight interconnected cubes and can fold and unfold cyclically. After three steps the eversion shows the cube again but with the initially hidden faces turned to the outside; in three more steps the figure turns back into its original state.[more]
Yoshimoto discovered that if there is a hole in the shape of a stellated rhombic dodecahedron inside the cube, the same shape appears on the outside after unfolding (Shinsei mystery). This Yoshimoto cube-star has therefore half of the volume of the cube. The cube can be separated into two rings of hinged solids such that one forms the outside of the cube with the described cavity and the other the star that fits into the cavity.
The same happens when the cavity has the shape of a truncated octahedron; the unfolded cube has the same shape as the hollow space.[less]
"The Yoshimoto Cube"
Wolfram Demonstrations Project
Published: March 7 2011