Helicopter cube was hand made, not 3d printed
Okamoto's original Bevel cube
(his site is now closed because all his designs were being KOd) was CNC milled from solid blocks of plastic, I believe.
Adam Cowan's Helicopter
(simultaneously invented) was 3D printed in ABS and hand smoothed with acetone.
Garrett 3D printed one
in ABS as well, I believe (acetone sealed).
TomZ 3D printed his non-curvy Helicopter in SLS.
I am not sure if anyone ever cast a helicopter, but it could certainly be done.
There is no puzzle one could easily mod into a Helicopter, it has a pretty unique geometry.
Jason Smith (io) produced an injection molded Helicopter cube based on Adam's design with his help.
So the Helicopter has been built by a few different methods, the first two being a combination of machine and hand production.