The inverted cube by Paul Schatz (1898-1979) is generated by means of three diagonal sections through a cube. These sections produce twelve equal, though not equal-sided, tetrahedrons.

When linked by linear joints, these tetrahedrons produce a chain which can be introverted through itself; this, when introverted, results in a cube and, when extraverted, in Kepler's packable rhombohedron with a cubic empty space. Both bodies are contained in the Metaeder.

According to Paul Schatz, this principle is applicable to all platonic solids, producing introvertable figurations in every case.

THE INVERTED CUBE IM METAEDER