The paper is devoted to various refinement strategies in the 4D Euclidean space. The red refinement strategy (RRS) have been widely used by researchers applying multigrid methods. This refinement method has a lot of advantages but it is not superior with respect to the degeneracy measure in the case of 3D quasi canonical domains, 3D ideal domains, 4D canonical domains and curved nonconvex domains. The RRS is compared with other subdivision methods for dividing ideal domains in the 4D Euclidean space. It is established that the RRS is superior than all other methods considered for all ideal domains.