Miura Map Folding and Unfolding

The Miura map fold (aka Miura-ori) is an example of a rigid origami model (can be folded from sheet metal with hinges instead of crease lines) which has applications in solar panel design for space satellites. This Demonstration offers a proof, of sorts, that the Miura map fold is rigid when made from a tiling of any nonsquare parallelogram.

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DETAILS

The folding angle represents the angle by which one specific crease is folded, which then determines the folding angles of all the other creases (folding angle = - the dihedral angle of the crease). The crease angle is the acute angle of the parallelogram which is tiled to make the crease pattern. The value crease angle = is a singularity of the folding equations; the creases cannot all collapse simultaneously when the parallelograms are perfect squares (they would have to be folded sequentially, like a regular road map). For some history of the Miura map fold, more information is online.

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