  Origami, the ancient art of folding thin sheets, has attracted increasing
attention for its practical value in diverse fields: architectural design,
therapeutics, deployable space structures, medical stent design, antenna design
and robotics. In this survey article we highlight its suggestive value for the
design of materials. At continuum level the rules for constructing origami have
direct analogs in the analysis of the microstructure of materials. At atomistic
level the structure of crystals, nanostructures, viruses and quasicrystals all
link to simplified methods of constructing origami. Underlying these linkages
are basic physical scaling laws, the role of isometries, and the simplifying
role of group theory. Non-discrete isometry groups suggest an unexpected
framework for the possible design of novel materials.
