AbstractThe mesh kernel for a star‐shaped mesh is a convex polyhedron given by the intersection of all half‐spaces defined by the faces of the input mesh. For all non‐star‐shaped meshes, the kernel is empty. We present a method to robustly and efficiently compute the kernel of an input triangle mesh by using exact plane‐based integer arithmetic to compute the mesh kernel. We make use of several ways to accelerate the computation time. Since many applications just require information if a non‐empty mesh kernel exists, we also propose a method to efficiently determine whether a kernel exists by developing an exact plane‐based linear program solver. We evaluate our method on a large dataset of triangle meshes and show that in contrast to previous methods, our approach is exact and robust while maintaining a high performance. It is on average two orders of magnitude faster than other exact state‐of‐the‐art methods and often about one order of magnitude faster than non‐exact methods.