On the Division of Abstract Manifolds in Cubes

We prove that in the class of abstract multidimensional manifolds without borders only torus $V_1^n$ of dimension $n\ge 1$ can be divided in abstract cubes with the property: every face $I^m$ from $V_1^n$ is shared by $2^{n-m}$ cubes, $m=0,1,\ldots,n-1$. The abstract torus $V_1^n$ is realized in $E^d$, $n+1\le d\le 2n+1$, so it results that in the class of all $n$-dimensional combinatorial manifolds [1] only torus respects this propriety. Torus is autodual because of this propriety.