3 31 Honeycomb - E7 Lattice

E7 Lattice

The vertex arrangement of 3₃₁ is called the E₇ lattice. contains as a subgroup of index 144. With the relation, the E₇ lattice can also be expressed as a union of the vertices of two A₇ lattices, also called A₇2:

= +

The E₇* lattice (also called E₇2) has double the symmetry, represented by ]. The Voronoi cell of the E₇* lattice is the 1₃₂ polytope, and voronoi tessellation the 1₃₃ honeycomb. The E₇* lattice is constructed by 2 copies of the E₇ lattice vertices, one from each long branch of the Coxeter diagram, and can be constructed as the union of four A₇* lattices, also called A₇4:

+ = + + + = dual of .