This paper is concerned with minimizing the cost of self-assembling DNA nanostructures. We first demonstrate that the octet truss provides an accurate geometric framework for current branched junction molecule assembly. We then develop a method of differentiating among junction molecules, the basic building blocks of the nanostructures themselves, within this structure. We use this approach to find the minimum number of junction molecules necessary to construct all of the platonic and archimedean solids naturally occurring within the octet truss
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