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Yeah, I took shell to exclude tension structures, rather thinking along the lines of concrete shells.
Yeah, classic numberphile video; where does it address whether saddles are better than domes, all I thought it said was that the Gaussian curvature of anticlastics are negative and synclastics are positive?
For some reason had it in my head that saddles where intrinsically more efficient a (concrete shell) structure than domes. Must be mistaken.
HHC
hamrack
I would suggest it depends on what you're building your structure from.
A synclastic shape (e.g. a dome) would be great for materials that are strong in compression (concrete, stone etc) but would be difficult to achieve with a material that is strong in tension (e.g. fabrics) as you are relying on an outward load (applied from the same side as the centres of curvature, e.g. differential air pressure) to apply tension to your material.
An anticlastic shape works well for materials strong in tension as you can apply large tensile preloads to the structure using a few members in compression.
So I wrote all that, and then realised I may have missed your point. This video may be relevant, it concerns gaussian curvature and why pringle/anticlastic shapes are sometimes better than synclastic shapes.
https://www.youtube.com/watch?v=gi-TBlh44gY