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The geometric space obtained by "gluing" a three-dimensional euclidean space using a group

The space E33 is defined, which is obtained by "gluing" Euclidean three-dimensional space using a uniformly discontinuous subgroup of the group of motions of Euclidean space, which is a direct product of three cyclic groups of parallel transfers. The main objects of the new space are determined and their affine and some metric properties are studied.