Hexadecachoric Honeycomb {3,3,4,3}

See http://en.wikipedia.org/wiki/16-cell_honeycomb Our Dodes125Tubes300DiagsSteelr is the 3d quasi-orthogonal projection of the F4 four-dimensional lattice. Each cell is linked to the 48 neighbors (24 sharing an octahedron, and 24 at distance square root of two, pi/4 rotated so they are the vertices of the dual 24-cell) This represent the space-time as an hyperdiamond crystal in a new theory of everything linked to quantum gravity. One half of F4 is the higgsonic bosonic part, the other is the gluonic bosonic part, the nonassociative compound is a fermion.