We find a closed-form expression for the Poisson's coefficient of curved-crease variants of the "Miura ori" origami tessellation. This is done by explicitly constructing a continuous one-parameter family of isometric piecewise-smooth surfaces that describes the action of folding out of a reference state. The response of the tessellations in bending is investigated as well: using a numerical convergence scheme, the effective normal curvatures under infinitesimal bending are found to occur in a ratio equal and opposite to the Poisson's coefficient. These results are the first of their kind and, by their simplicity, should provide a fruitful benchmark for the design and modeling of curved-crease origami and compliant shell mechanisms. The developed methods are used to design a curved-crease 3D morphing solid with a tunable self-locked state.
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