PMC

a) It is highly improbable that 12 free-floating pentagonal panels will self-assemble to form a hollow dodecahedron. b) Tethering limits the number of possible self-assembly outcomes and can be used to construct a hollow dodecahedron with higher probability.

(a) TEM micrograph of icosahedral nanoparticles in the α-Mg matrix of as-cast Mg–8.3Zn–0.7Y alloy; (b)–(d) the projected morphologies of the I-particles and corresponding schematic drawings of a pentagonal dodecahedron, which is projected along its five-, three- and two-fold symmetry axes, respectively []. © IOP Publishing. Reproduced by permission of IOP Publishing. All rights reserved.

(A) Recombinant BgAChBP1 pentamers (short arrow) and dodecahedra (large arrows). Left insert, enlarged view along the five-fold symmetry axis of a recombinant dodecahedron and a single pentamer, respectively. Right insert, 3D reconstruction (resolution ∼20 Å) from ∼3000 negatively stained particles of the recombinant BgAChBP1 dodecahedron. (B) Recombinant BgAChBP2 pentamers (short arrow) and presumed di-pentamers (large arrows). In several independent expression experiments, not a single dodecahedron was detected in the electron microscope.

(Color online) Image and net representations of (a) the icosahedron, (b) the snub dodecahedron, (c) the snub cube, (d) the great rhombicosidodecahedron, (e) the triangular prism, (f) the square antiprism, (g) the gyroelongated pentagonal birotunda, and (h) the pentagonal hexecontahedron. Polyhedron (a) is a Platonic solid, polyhedra (b), (c), and (d) are Archimedean solids, polyhedron (e) is a prism, polyhedron (f) an antiprism, polyhedron (g) a Johnson solid, and polyhedron (h) a Catalan solid. The Catalan solid in (h) is the dual of the Archimedean solid in (b), and the polyhedra in (b), (c), (g), and (h) are chiral.