Riddles alive in space

While studying the laws of inversion, Paul Schatz also discovered a large number of new and interesting solids created by the movements of the edges, corners, and diagonals of cubes. Paul Schatz called them time or polysomatic forms, as they render the movement of inversion visible in space.

These forms - such as the inversion hall, the edge-cuboid, the pole-cuboid, or others - show some relation to living forms seen in nature. Time and again, Paul Schatz sought to apply these forms to architecture and his own architectonic designs.
 
Pole-cuboid cut in half (or "Inversion Hall") as a three-dimensional shape
 
More about objects and principles of forms by Paul Schatz:

Polysomatic Forms
The Geometry of Space
The Invertible Cube
The Oloid
The Inversina
Further Developments