A geometric space obtained by "gluing" a three-dimensional Euclidean space using a group that is a direct product of three subgroups of parallel transfers

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 deter-mined and their affine and some metric properties are studied.