Using isometries in design and fabrication

There's a cool new paper by Caigui Jiang, Hui Wang, Victor Ceballos Inza, Felix Dellinger, Florian Rist, Johannes Wallner, and Helmut Pottmann. Would you have believed an independently-designed, sleek, freeform shape like in the picture above could be assembled from a small alphabet of curved surface patches? The secret is to allow the patches to bend isometrically, that is with constant intrinsic (Gaussian) curvature--as thin shells naturally tend to do--vastly extending the design space of a small set of tools. Bravo!