Believed to be the most geometrically complex and aesthetically beautiful structure in mathematics, the 4_21 polytope is the algebraic form at the centre of a universal theory of everything. Originally described in the late 19th century, 4_21 models all interactions and transformations between known and postulated sub-atomic particles. It is the 21st century equivalent of the proto-scientific art of alchemy ? where the transmutation of elements was the most elusive mystery of the universe. The theory is an attempt to reconcile one of the fundamental unsolved problems in physics: unify quantum physics and gravitation in hopes of ultimately explaining the fabric of the universe.