How to construct a block with four vertices
 

Generally a block needs 8 vertices, but now I have to tackle the intersection of two cylinders with equal diameters. The intersection part can be seen as four polyhedrons, each of which has four vertices and four surface.

I found block with six vertices constructed from page 136 of User Guide for OpenFOAM 1.5. But does anyone know if it is possible to construct block with four vertices?

Thanks in advance!