Uniform refinable 3D grids of regular convex polyhedrons and balls (Q1714961)

Using a simple volume-preserving map from the cube to a tetrahedron, an equal-volume subdivision of arbitrary convex polyhedrons into polyhedral cells is constructed. Moreover, mapping the regular octahedron onto the ball using a volume-preserving map previously constructed by the authors, one can obtain uniform and refinable grids on the 3D ball by a similar procedure, starting from appropriate grids on the cube.