Geodesic
On the Division of Abstract Manifolds in Cubes
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2006), pp. 29-34 
Mariana Bujac; Sergiu Cataranciuc; Petru Soltan. On the Division of Abstract Manifolds in Cubes. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2006), pp. 29-34. http://geodesic.mathdoc.fr/item/BASM_2006_2_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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