The 4D mesh generated by the 'satori' algorithm, and Voronoi regions of its nodes

The data contained in the archive is the 4D mesh containing 5^4 translation units, that are 2^4 points of tesseract shifted with 'satori' algorithm (total 10 000 nodes), and Voronoi diagram calculated using the qhull package for these points.

It is used to demonstrate the shape uniqueness of the 4096 diagram's inner regions. The tessellation of inner regions is a candidate to be a solution of Kelvin problem in 4D version, offering possible minimal interface hyper-area to hyper-volume ratio. The structure posesses PT-symmetry so it might have applications in particle physics. For instance, its 3D layers can be used as CPT-compatible cellular automata for 3D simulations in chiral space.

Presumably, the structure can be self-assembling in conditions near to critical point of second order phase transitions.