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 V1n of dimension n≥1 can be divided in abstract cubes with the property: every face Im from V1n is shared by 2n−m cubes, m=0,1,…,n−1. The abstract torus V1n is realized in Ed, n+1≤d≤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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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. https://geodesic-test.mathdoc.fr/item/BASM_2006_2_a2/

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