A novel efficient four-dimensional foam and its application in computational particle modeling

A problem of finding space partitioning into cells of equal volume with the least area of surface between them was established by Lord Kelvin\footnote{Lord Kelvin (Sir William Thomson). Phil. Mag. \textbf{24}, 151 (1887)} in 1887 in a framework of the ether theory. The problem still has the proven\footnote{Hales, Thomas C. Discrete Comput. Geom. \textbf{25}, 1 (2001)} solution just for 2D space, that is a regular hexagon tiling. Original Kelvin conjecture in 3D, that is the bitruncated cubic honeycomb, got the counterexample\footnote{Weaire D., Phelan R. Phil. Mag. Lett. \textbf{69}, 2 (1994).} in 1993. We propose the candidate solution for the Kelvin problem in 4D that appears more simple and more efficient than the best known 3D solution. It is a regular foam of uniform 26-cell polytopes. Its properties allow us to consider it as a prospective basic spacetime computational model possessing CPT symmetry. Some anti-structure defects of this tessellation could be mapped to known SM fundamental particles manifesting correct quantum numbers\footnote{Dmitrieff E.G. Proc. 21th Workshop “What comes beyond the SMs”(2018)}. We discuss arguments in favor of generalizing the original problem to be any-dimensional, and existing of the only solution of it, namely one we proposed.