The E8 HyperDiamond lattice is used to construct the HyperDiamond Feynman Checkerboard model.
±1, ±i, ±j, ±k, ±e, ±ie, ±je, ±ke, (±1±ie±je±ke)/2, (±e±i±j±k)/2, and the last two with cyclical permutations of {i,j,k,e,ie,je,ke} in the order (e, i, j, ie, ke, k, je).
The E8 lattice in R8 has a counterpart in C4, the self-reciprocal honeycomb of Witting polytopes, a lattice of all points whose 4 coordinates are Eisenstein integers with the equivalent congruences