Getting rid of the diagonals is tricky as the hardware is likely to only draw triangles and it would be difficult to determine which edge is the diagonal. Alternatively, you could apply a wireframe texture (or a shader that generates a suitable texture). That would solve the hidden line issues, but would look odd as the thickness of the lines would be dependant on z distance.
The built-in wireframe mode renders edges of the primitives. As in D3D the primitives are triangles (or lines, or points - but not arbitrary polygons), that means the built-in way won't cut it.
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