Amazing Geometry Machine

Oscillating tri-colored tetrahedra based on
The above illustration is an idealized animation of one embodiment discovered using DPTM Modeling.

Originally published:
Forma, Vol. 15 (No. 2), pp. 149-155, 2000 SciPress PDF 

Dynamic Polystring Transformahedra Modeling (DPTM), invented by Richard Esterle, U.S. Patent 5,316,483 is a new modeling concept in the exploration of 3-dimensional space in general and polyhedra specifically. In DPTM, polyhedra related structures are built with tubes passing through a polyhedral core and colored loops of string through those tubes creating the edges of a resulting polyhedron,  often its dual polyhedra. The color patterns may mirrotate at opposite ends of the tubes, as well as opposing faces of the polyhedra due to intrinsic structural requirements of the modeling process. The polyhedra deform and/or interpenetrate as a result of sliding the tubes inline (inline translation).