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In 1984, Dancis proved that any $d$-dimensional simplicial manifold isdetermined by its $(\lfloor d/2 \rfloor + 1)$-skeleton. This paper adapts hisproof to the setting of cubical complexes that can be embedded into a cube ofarbitrary dimension. Under some additional conditions (for example, if thecubical manifold is a sphere), the result can be tightened to the $\lceil d/2\rceil$-skeleton when $d \geq 3$.

Reconstructing $d$-manifold subcomplexes of cubes from their $(\lfloor d/2 \rfloor + 1)$-skeletons