Topological phases derived from point degeneracies in photonic band structures show intriguing and unique behavior. Previously identified band degeneracies are based on accidental degeneracies and subject to engineering on a case-by-case basis. Here we show that deterministic pseudo Weyl points with nontrivial topology and hyperconic dispersion exist at the Brillouin zone center of chiral cubic symmetries. This conceivably allows realization of topologically protected frequency isolated surface bands in 3D and n=0 properties as demonstrated for a nanoplasmonic system and a photonic crystal.