Axial (helical) substructures determined by the root lattice E8 as generating clusters of the condensed phases

Abstract The most complete symmetry description of the close-packed structures can be achieved by the use of the 8-dimensional root lattice E 8 which determines the {3, 3, 5} polytope (4-dimensional counterpart of an icosahedron). The helix substructure of the {3, 3, 5} polytope can be delineated when the centers of the icosahedra form the 15/4 spiral. The topologically equivalent helix is realized in the structure of the A13 type (β-Mn). The hypothesis is put forward that melting of metals is realized as the transformation from the periodic crystalline packing to the non-periodical helix packing described by a non-classical symmetry axis. Experimental evidences for this hypothesis are indicated.