In these pictures you can see eight slice forms (the template is from John Sharp’s book Sliceforms). Sliceforms are made of paper and can be folded to lie down flat. They can be constructed by modelling the object in 3D and then cutting out equidistant vertical slices and repeating that perpendicularly. Then they are printed out, cut out and assembled. This should work with pretty much any surface/form you like. I think Model 6, the Conoid Surface, is particularly interesting, as the purple slices are all straight lines. The blue slices could do the same and you still get this curvy looking hyperbolic paraboloid.
Nadja is a Mathematics and Statistics Undergraduate in the Mathematical Institute and Department of Statistics, University of Oxford.