Twisted Cylinder (Hyperboloid of one sheet) I want to create a mesh like this:



with a vertex on every edge-crossing so that every face is kite (nearly rhombus) shaped.

The above image was created just by rotating the top of two cylinders in different directions and placing them on the same position.



But here I wouldn't have these many small faces and the result of the overlapping twisted cylinders looks like this in solid display:



Can you please tell me if there is a way the create these kite-faces. Is there a tool that automatically creates a new vertex and a face for every intersection of edges?
I think this solves the issue with moonbots answer. Use the TinyCAD addon to create vertices at the edge itersections

EDIT steps:


rotate top face 90 degrees (R, Z, 90)
duplicate (Shift-D) and mirror along any axis (e.g. Ctrl-M, X)
press W and select TinyCAD ⯈ XALL
press F to fill faces
press W and select Remove Doubles