Geometrically protected triple-point crossings in an optical lattice

We show how to realize topologically protected crossings of three energy bands, integer-spin analogues of Weyl fermions, in three-dimensional optical lattices. Our proposal only involves ultracold atom techniques that have already been experimentally demonstrated, and leads to isolated triple point crossings (TPC) which are required to exist by a novel combination of lattice symmetries. The symmetries also allow for a new type of topological object, the type-II, or tilted TPC. Our work shows that spin-1 Weyl points, which have not yet been observed in the bandstructure of crystals, are within reach of ultracold atom experiments.