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The Pfeiffer Cube is probably the best known of all invertible forms. This simple cube of eight smaller cubes was patented by Peter-Michael Pfeiffer in 1964 (DE). It has since then been a very successful retail and promotional item.
Its cycle of inversion involves six successive simple hinged movements - in stark contrast to models such as the Schatz Cube, which invert in a single harmonious flowing motion.
As shown here, three simple hinged movements invert the Pfeiffer Cube in that its outer (dark) surfaces have all become inner surfaces and its inner (light) surfaces have become outer surfaces. It also inverts in the sense that each element of the cube passes through the centre of the model during inversion. A further three simple hinged movements IN THE SAME DIRECTION lead again to the original orientation of the cube.
There are other cubes of eight elements which can be inverted in an identical manner.
Remarkably, it is possible to divide each element of this cube into two identical pieces to form two separate models which can be inverted with the same motion, both separately and simultaneously. The best known division of the Pfeiffer Cube is the StarCube (also known as Slothouber Cube, Yoshimoto 1 and Shinsei Mystery).
Two other known divisions into identical parts are the Truncated Octahedron (mentioned in section 9.4 of Jay Kapraff's book, Connections) and the 64 Cube(each of the eight cubes is divided further into eight smaller cubes). Both of these forms differ from the StarCube in that both of the models produced by division are visible at all times. Yhe following illustrations show how the elements are divided in these two cases and the twin states of the two models. Note that the lengths of the hinges are halved in each of these models.
Two methods of partitioning the elements of the Pfeiffer Cube into identical pairs are shown above. The completed model pairs are shown below.