 Cube flux from a corner charge

For a point charge exactly at a cube corner, each of the three opposite faces has outward electric flux $q/(24{ϵ}_0)$. Reflecting the cube in its three incident faces makes a larger cube centred on the charge and proves the result by symmetry. The three incident faces have zero normal electric field away from their singular corner. Their improper integrals vanish; the total is $q/(8{ϵ}_0)$. This boundary convention differs from moving a charge to the corner from the interior after computing a closed-surface integral.