This is a model of part of a helicoid with parametric equations x(t)=u.cos(t), y(t)=u.sin(t), and z(t) = 2t/3, where the parameter u goes between -1 and 1. The parameter t goes between 0 and Pi for the half-twist, goes between 0 and 2Pi for the full-twist.
This model was designed and printed by my WLU summer research student Emily Jaekle ('16). See http://mathvis.academic.wlu.edu/2015/07/27/helicoids/.
We printed these helicoids on a FormLabs Form 1+ liquid resin printer. The half-twist helicoid was printed in black resin (0.1mm slices), the full-twist helicoid in clear resin (0.2mm slices). The print was excellent in both cases. (The .form files we used are included.)
Note: we had tried to print the half-twist on the MakerBot 2X, but had two fails. It might well print if additional supports are added - however we haven't figured this out.