Imagine a coordination polyhedron with a cation at the center. Now treat the ions as hard spheres and reduce the size of the cation until the anions just touch. What is the radius r of the cation for anions of unit radius in the following coordinations: 

(a) Cube, 

(b) Octahedron,

(c) Tetrahedron. 

Body diagonal is √3 and face diagonal √2 times the cube edge.