Our communication is devoted to the construction of a countable series of hyperbolic 3-manifolds for which a fundamental polyhedron P has right angles, is unbound, but has finite volume. Polyhedra P have both proper vertices and infinitely remote vertices. First we construct a countable series of polyhedra with all dihedral angles of ¼=2. Then we give motions that identify faces of these polyhedra and show that generated by these motions groups ¡ are torsionfree. Factorizing H3 by groups ¡ we obtain non-compact 3-manifolds with finite volume. The polyhedra P contain 4p faces which are hexagons with two infinitely remote and four proper vertices. There are two faces which are regular 4p¡gons with all the vertices being on the absolute (upper and bottom bases). Also a polyhedron P has 4p faces which are triangles with one proper vertex and two improper vertices and they are adjacent to bottom base, and P has 4p analogous triangular faces adjacent to upper base of the polyhedron where p = 1; 3; :::. Denote by ®i hexagonal faces of the polyhedron P, by ¯i triangular faces adjacent to upper base and by °i triangular faces adjacent to the bottom base of polyhedron P where i = 1; 2; :::; 4p. Let ¿1 denote the bottom base and ¿2 denote the upper base of the polyhedron P. Indicate motions which identify faces of polyhedra. Every face ®i with odd number is identified, by Ái a helical motion with rotation angle of ¼, with the opposite face ®i+2p. Every face ®i with even number is identified by Ái a translation with the opposite face. Every face °i is identified by a translation 'i with the face ¯i, where i = 1; 2:::; 4p. Finally face ¿1 is identified with the face ¿2 by a helical motion ± with rotation angle of ¼.We show that under these conditions the group ¡ generated the motions Ái, 'i and ±, i = 1; 2; :::; 4p, is torsion-free and, therefore, factorizing the hyperbolic space H3 by the groups ¡ we obtain a countable series of manifolds M = H3=¡. These manifolds are non-compact, but have finite volume, and all the dihedral angles of fundamental polyhedron for these manifolds are equal to ¼=2.