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The purpose of this paper is twofold. First, by means of computer graphics, we construct pictures of the representative cases of the helicoidal surfaces of constant mean curvature. At the same time, we depict their periodic isometric deformation into Delaunay surfaces under preservation of the mean curvature. Second, we prove new properties of these surfaces--we find necessary and sufficient conditions so that they become dense or closed inside the solid cylindrical shell in which they lie. Key words: constant mean curvature, helicoidal surfaces
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