Geodesic
Three-Dimensional Manifolds Defined by Coloring a Simple Polytope
Matematičeskie zametki, Tome 69 (2001) no. 3, pp. 375-382.

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In the present paper we introduce and study a class of three-dimensional manifolds endowed with the action of the group $\mathbb Z_2^3$ whose orbit space is a simple convex polytope. These manifolds originate from three-dimensional polytopes whose faces allow a coloring into three colors with the help of the construction used for studying quasitoric manifolds. For such manifolds we prove the existence of an equivariant embedding into Euclidean space $\mathbb R^4$. We also describe the action on the set of operations of the equivariant connected sum and the equivariant Dehn surgery. We prove that any such manifold can be obtained from a finitely many three-dimensional tori with the canonical action of the group $\mathbb Z_2^3$ by using these operations. 
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I. V. Izmest'ev. Three-Dimensional Manifolds Defined by Coloring a Simple Polytope. Matematičeskie zametki, Tome 69 (2001) no. 3, pp. 375-382. http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a6/

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