Planar mesh refinement cannot be both local and regular
The result of this paper is stated in the title and refers to triangular meshes being regular in the sense that every interior vertex has degree 6, and hence the interior part of the mesh can be mapped onto a standard mesh consisting of equalised triangles. The proof covers a stronger result, namely that the refinement of a regular mesh cannot be both regular and strictly interior. As the authors stress, their consideration is restricted completely to planar meshes.
scientific article; zbMATH DE number 1145970