Metamorphosis of a Cube
Paul Schatz (1898–1979), a German engineer, invented this fascinating transformation of a cube. The cube is separated into three parts of equal volume, two of which have the same shape (Schatz called them "Riegel", meaning latch or bolt); they contain opposite vertices of the cube. The third part (called "Gürtel", or belt), consists of six rectangular tetrahedra, where adjacent ones have a common edge. The tetrahedra form a kaleidocycle, which means that it can be transformed so that the inside can be turned to the outside and vice versa. Paul Schatz called the cube "umstülpbarer Würfel" which means an eversible cube.[more]
You can separate the three parts with the shift slider or rotate them about the axis. You can evert the middle part, but only if the shifted parts are out of the way. A top view of this transformation is provided. Because the "Riegel" parts are not so interesting, they can be moved out of sight.[less]
There is a lot of material available about Paul Schatz and kaleidocycles, such as .
"Metamorphosis of a Cube"
Wolfram Demonstrations Project
Published: January 8 2009