This paper presents an automated meshing technique for periodic composites using hierarchical tri-quadratic tetrahedral elements. The method addresses the challenge of manual mesh generation in complex material arrangements, which can be a significant obstacle in computational homogenization. The approach starts with a hierarchical pixel or voxel mesh and evolves it into a final mesh that accurately captures material arrangements, constituent volume fractions, and stress-strain fields under various loading conditions. The techniques are demonstrated on densely packed fiber and particulate composites, as well as 3D textile-reinforced composites. The paper discusses the challenges of two-way meshing and external face-matching in periodic media, and proposes a solution using material domain identification functions (MDIFs) and nodal shifting. The effectiveness of the method is demonstrated through convergence studies on different composite types, showing that the proposed meshing techniques provide accurate and efficient results.This paper presents an automated meshing technique for periodic composites using hierarchical tri-quadratic tetrahedral elements. The method addresses the challenge of manual mesh generation in complex material arrangements, which can be a significant obstacle in computational homogenization. The approach starts with a hierarchical pixel or voxel mesh and evolves it into a final mesh that accurately captures material arrangements, constituent volume fractions, and stress-strain fields under various loading conditions. The techniques are demonstrated on densely packed fiber and particulate composites, as well as 3D textile-reinforced composites. The paper discusses the challenges of two-way meshing and external face-matching in periodic media, and proposes a solution using material domain identification functions (MDIFs) and nodal shifting. The effectiveness of the method is demonstrated through convergence studies on different composite types, showing that the proposed meshing techniques provide accurate and efficient results.