I was thinking about corkscrews and in 3d a corkscrew is a line drawn along a cylinder. The x and y coordinates of a corkscrew repeat an infinite number of times but a corkscrew does not curve back in on itself because the z coordinate never repeats. Because the Doucylinder is basically a cylinder that curves back in on itself it is possible to have a kind of corkscrew along its surface that does curve back in on itself. Not only do the x and y coordinates repeat for a corkscrew drawn on a duocylinder but the z and w coordinates also repeat. The equation for a corkscrew drawn on a duocylinder is
x=sinat
y=cosat
z=sinbt
w=cosbt