In this fascinating article, Roice Nelson showcases the stunning hexagonal tiling honeycomb, a unique structure that fills 3D space with polyhedra in a symmetrical manner. Regular honeycombs exhibit geometric symmetries that act transitively on flags, like the {4,3,4} cubic honeycomb in Euclidean space. Surprisingly, the hexagonal tiling honeycomb, denoted {6,3,3}, features flat Euclidean planes in hyperbolic space, each containing an infinite number of regular hexagons. The connection to hyperbolic space, special relativity, and 2×2 hermitian matrices is explored, leading to a groundbreaking conjecture on the hexagonal tiling honeycomb’s placement in Minkowski spacetime. This insightful piece delves into complex mathematical concepts with elegance and depth.
https://johncarlosbaez.wordpress.com/2024/05/04/hexagonal-tiling-honeycomb/