  We prove that the 8-point algorithm always fails to reconstruct a unique
fundamental matrix $F$ independent on the camera positions, when its input are
image point configurations that are perspective projections of the vertices of
a combinatorial cube in $\mathbb{R}^3$. We give an algorithm that improves the
7- and 8-point algorithm in such a pathological situation. Additionally we
analyze the regions of focal point positions where a reconstruction of $F$ is
possible at all, when the world points are the vertices of a combinatorial cube
in $\mathbb{R}^3$.
