We generalize the massless Dirac equation and Weyl equation to give particles with internal symmetry of the Standard Model fermions. The 2x2 or 4x4 complex matrices are matrix rings $R$ and can be generalized by a group $G$ to a group algebra $G[R]$. For a group of size N, this creates N times as many Pauli spin or gamma matrices and generalizes the wave equations. We consider point group symmetries for $G$ and show that using the full octahedral group and the 2x2 complex matrices gives a group algebra which generalizes the Weyl equation to the Standard Model fermions plus a dark matter particle. An alternative is to use the chiral octahedral group and the 4x4 complex matrices to generalize the massless Dirac equation. The method leaves a dark matter particle and its antiparticle. We describe the symmetry of dark matter.