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Practical components for three-dimensional molecular nanofabrication must be simple to produce, stereopure, rigid, and adaptable. We report a family of DNA tetrahedra, less than 10 nanometers on a side, that can self-assemble in seconds with near-quantitative yield of one diastereomer. They can be connected by programmable DNA linkers. Their triangulated architecture confers structural stability; by compressing a DNA tetrahedron with an atomic force microscope, we have measured the axial compressibility of DNA and observed the buckling of the double helix under high loads.