We present an extension of the earthquake simulation software SeisSol to support seismic wave propagation in fully triclinic anisotropic materials. To our best knowledge, SeisSol is one of the few open-source codes that offer this feature for simulations at petascale performance and beyond. We employ a Discontinuous Galerkin (DG) method with arbitrary high-order derivative (ADER) time stepping. Here, we present a novel implementation of fully physical anisotropy with a two-sided Godunov flux and local time stepping. We validate our implementation on various benchmarks and present convergence analysis with respect to analytic solutions. An application example of seismic waves scattering around the Zugspitze in the Bavarian Alps demonstrates the capabilities of our implementation to solve geophysics problems fast.