Geodesic
On the Division of Abstract Manifolds in Cubes
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2006), pp. 29-34

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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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     title = {On the {Division} of {Abstract} {Manifolds} in {Cubes}},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
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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/