We describe the space ∑\
olimits_H of all surfaces in {R^3} that have constant mean curvature H \
e 0 and are invariant by helicoidal motions, with a fixed axis, of {R^3}. Similar to the case ∑\
olimits_0 of minimal surfaces ∑\
olimits_H behaves roughly like a circular cylinder where a certain generator corresponds to the rotation surfaces and each parallel corresponds to a periodic family of isometric helicoidal surfaces.
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