AbstractMotivated by the need for fast robust generation of unstructured grids comprised entirely of hexahedral cells, we approach the issue via an intermediate tetrahedral discretization. This is then followed by subdivision of the tetrahedra into hexahedra and in this note we focus on the geometric construction, properties and limitations of a ‘best subdivision’ to ‘Hex the Tet’. Related issues include the appropriate choice of edge, face and interior points, convexity of the resulting face quadrilaterals and associated hexahedra for all tetrahedra shapes and validity and shape quality of the final hexahedra. Copyright © 2002 John Wiley & Sons, Ltd.