Square-Pinwheel Tessellations (Flat & Curved)
To conserve my uploading restrictions for the month, I've combined all 4 relevant photos for this into one (I strongly advise using the larger view, especially if you expect to see the CP).
Top left: CP's for both the flat version and the curved version.
Top right: Flat version backlit.
Bottom right: Flat version not-backlit
Bottom left: Curved version
(Flat version folded from 3" white kami, curved version from 8.5" square printing paper)
This evolved as s 4-sided version of this:
Getting the angles to work out was actually much more confusing than I had anticipated (though this was probably much amplified because this was my first square-based tessellation). Look at the flat-cp to see the use of weirdly oriented right-isosceles triangle twists. Also note the grid of 19ths; it needs an odd number the way I have it set-up.
I used splines to generate guesstimated curves for the 3-D version, but in reality the curves should probably all be elliptical arcs.