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Polynuclear metal clusters, particularly those with aesthetically appealing structures, are of increasing interest. In this study, by employing C4 symmetrical macrocyclic silsesquioxane ligand, a novel tridecanuclear Gd(III) cluster (Gd13) with a {Gd13O8} core featuring unprecedent body-centered Archimedean cuboctahedron conformation is realized using an efficient solvothermal method instead of conventional Schlenk techniques. To the best of our knowledge, Gd13 cluster is thus far the highest nuclearity of lanthanide-silsesquioxane. Moreover, a magnetic study reveals a weak antiferromagnetic interaction between adjacent Gd ions in the cluster. In addition, Gd13 exhibits cryogenic magnetocaloric effects with a maximum −ΔSM value of 20 J kg−1 K−1 at 2 K and ΔH = 7.0 T.

Summary The design principle of supramolecular architectures through a bottom-up strategy has always been guided by polyhedra such as Platonic solids, Archimedean solids, and prisms (antiprisms) with high symmetry. Non-uniform convex polyhedra with regular faces, i.e., Johnson solids, are rarely constructed experimentally although their topologies have been predicted through mathematical theory. Herein, self-assembly of a giant triangular orthobicupola [Zn24612], one of 92 Johnson solids J27, has been achieved from the coordination between 24 Zn2+ and 12 tetrakis-terpyridine building blocks 6 in DMF (N,N-Dimethylformamide). Different from classical Oh or Td symmetric cuboctahedron, the structure of this triangular orthobicupola revealed D3 symmetry which has been unambiguously determined by synchrotron X-ray analysis, NMR, and mass spectrometry. Surprisingly, the self-assembly process has been found to be solvent dependent. The same Zn2+ and tetrakis-terpyridine ligand 6 assembled into another pentagonal prism with the composition of [Zn20610] when using methanol as the reaction solvent.

The problem of classifying orientable vertex-transitive maps on a surface with genus two is considered. We construct and classify all simple orientable vertex-transitive maps, with face width at least 3 which can be viewed as generalisations of classical Archimedean solids. The proof is computer-aided. The developed method applies to higher genera as well.

We report star polyhedral gold nanocrystals synthesized by colloidal reduction with ascorbic acid in water at ambient conditions. We identify two distinct classes of star nanocrystals: multiple-twinned crystals with fivefold symmetry, and monocrystals. These respective classes correspond to icosahedra and cuboctahedra, two Archimedian solids, with preferential growth of their {1 1 1} surfaces. Due to this preferential growth, the {1 1 1} faces of the original Archimedean solids grow to become tetrahedral pyramids, the base of each pyramid being the original polyhedral face. By assuming a star morphology, gold nanocrystals increase their proportion of exposed {1 1 1} surfaces, which possess the lowest surface energy among low-index crystallographic planes for FCC crystals. Thus, we propose that the driving force for star nanocrystal formation could be the reduction in surface energy that the crystals experience. Interestingly, icosahedrally derived star nanocrystals possess a geometric morphology closely resembling the great stellated dodecahedron, a Kepler-Poinsot solid. r 2005 Elsevier B.V. All rights reserved. PACS: 61.46.+w; 81.07.Bc; 68.37.Lp; 68.37.Hk

Strategies for the design of multimolecular hosts that display recognition properties analogous to those of monomolecular predecessors are described. In particular, the bowl-shaped cavity of a molecular receptor known as resorcin[4]arene has been elaborated, using hydrogen bonds, for the construction of open and closed cavities that accommodate single and multiple guest species. Both chemical and geometric considerations derived from these studies have led us to identify host frameworks, based upon the five Platonic and 13 Archimedean solids, which have yet to be synthesized or discovered and we propose such systems as targets in chemical synthesis.

The uniform polyhedra form a fascinating set of objects for display on graphics output devices. When animated on graphics screens they help in visualization of three-dimensional structures and in understanding the geometrical properties and relationships between the various polyhedra. However, the coordinates of the vertices of these objects—the Platonic solids, the Archimedean solids, the Johnson solids and the starred regular polyhedra—are mostly very difficult and tedious to determine algebraically. When the objective is simply to display these solids on a graphics screen, rather than explicit coordinate calculation, another approach can be adopted: the use of jet graphics software. Turtle graphics provides a compact method of describing and displaying the two-dimensional analogies of these solids, and this research investigated to what extent three-dimensional turtle graphics, also known as jet graphics, could describe and also display the regular three-dimensional polyhedra. A number of methods applicable to many of the solids were invented. In particular, methods were found that apply to the infinite classes of prisms and anti-prisms, pyramids and dipyramids, cupolas, bicupolas and gyrobicupolas as well as some starred versions of these polyhedra. A new class of polyhedra, the star antiprisms, are shown to be facially equilateral only for the case when the parallel faces correspond to pentagrams. A single iterative algorithm for the finite class of convex regular polyhedra was found. However, this method applies to all Platonic solids except the icosahedron, and generalizes the Petrie polygon rings to form new infinite classes of polyhedra such as Petrie-prisms. A recursive algorithm is described which correctly displays all regular polyhedra and is generalizable to semiregular and other classes of polyhedra.

Theoretical evidence is presented for the stability of C 120 and C 60 molecules consisting of sp 2 hybridized carbon atoms only. These spherical shell molecules have the structures of two of the thirteen Archimedean solids. Simple Huckel molecular orbital calculations show that there is a large, stabilizing, delocalization energy.

A regular-faced convex polyhedron is one in which all the faces are regular polygons, not necessarily with the same number of sides. Counting the prisms and anti- prisms as one type of solid each, there seem to be 112 regular-faced convex polyhedra as conjectured by Johnson and later proved by Zalgaller. These polyhedra can all be built from combinations of 28 simple polyhedra plus prisms and antiprisms. The properties of these solids including the volume and sphericity are presented. The methods and problems in determining the number of these solids are given. Photographs of all the solids are shown. Nets for construction of the polyhedra are given, as well as methods of construction.