Geodesic
On the cubic complexity of three-dimensional polyhedra
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 245-250

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A cubulation of a three-dimensional polyhedron $P$ is understood as a finite family of copies of the standard oriented cube in $\mathbb R^3$ and of orientation-changing isometries of its faces such that the result of gluing together these isometries of the cubes is homeomorphic to $P$. We prove that any three-dimensional polyhedron represented by a cubulation consisting of $n$ cubes possesses a standard triangulation consisting of $6n$ tetrahedra.
Mots-clés : polihedron, triangulation
Keywords: 3-manifold, cubulation, Matveev complexity, cubic complexity. 
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V. V. Tarkaev. On the cubic complexity of three-dimensional polyhedra. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 1, pp. 245-250. http://geodesic.mathdoc.fr/item/TIMM_2011_17_1_a19/