A Theorem of Newton (April 2008)

DNA-caged nanoparticles via electrostatic self-assembly

“…The hexagonal nature of these DNA tiles does not allow for the complete formation of a sphere as stated by Euler's formula V − E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces. 30 A sphere comprised of hexagons must include at least 12 pentagons. Thus, these DNA tiles will not form perfect interlocking structures, but this is not necessary, as the combination of electrostatic interactions and physical interlocks stabilizes the structure.…”