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Nature 460, 876-879 (2009) In the Introduction and in the Figure 4 legend of this letter, it was stated that the truncated tetrahedron is the only Archimedean solid that is [...]

The paper is devoted to perfect and almost perfect homogeneous polytopes in Euclidean spaces. We have classified perfect and almost perfect polytopes among all regular polytopes and all semiregular polytopes except Archimedean solids and two four-dimensional Gosset polytopes. Also we have constructed some non-regular homogeneous polytopes that are (or are not) perfect and posed some unsolved questions., Author(s): V. N. BerestovskiÄ­ [sup.1], Yu. G. Nikonorov [sup.2] Author Affiliations: (1) grid.426295.e, 0000 0004 0620 109X, Sobolev Institute of Mathematics of the SB RAS, , 4 Acad. Koptyug Ave., [...]

Author(s): Todd O. Yeates Author Affiliations: Protein assembles into Archimedean geometry A combination of ideas from geometry, computer science and molecular biology is ushering in a golden age for the [...], A natural protein has been engineered to self-associate into an architecture previously unknown among biological molecules: a cage structure based on one of the classic polyhedra identified by Archimedes. How to engineer a protein to make an extraordinary cage structure.

Author(s): Ali D. Malay [sup.1] [sup.14] , Naoyuki Miyazaki [sup.2] , Artur Biela [sup.3] [sup.4] , Soumyananda Chakraborti [sup.3] , Karolina Majsterkiewicz [sup.3] [sup.5] , Izabela Stupka [sup.3] [sup.5] , [...], Symmetrical protein cages have evolved to fulfil diverse roles in nature, including compartmentalization and cargo delivery.sup.1, and have inspired synthetic biologists to create novel protein assemblies via the precise manipulation of protein-protein interfaces. Despite the impressive array of protein cages produced in the laboratory, the design of inducible assemblies remains challenging.sup.2,3. Here we demonstrate an ultra-stable artificial protein cage, the assembly and disassembly of which can be controlled by metal coordination at the protein-protein interfaces. The addition of a gold (i)-triphenylphosphine compound to a cysteine-substituted, 11-mer protein ring triggers supramolecular self-assembly, which generates monodisperse cage structures with masses greater than 2 MDa. The geometry of these structures is based on the Archimedean snub cube and is, to our knowledge, unprecedented. Cryo-electron microscopy confirms that the assemblies are held together by 120 S-Au.sup.i-S staples between the protein oligomers, and exist in two chiral forms. The cage shows extreme chemical and thermal stability, yet it readily disassembles upon exposure to reducing agents. As well as gold, mercury(ii) is also found to enable formation of the protein cage. This work establishes an approach for linking protein components into robust, higher-order structures, and expands the design space available for supramolecular assemblies to include previously unexplored geometries. An artificial protein cage is readily assembled by metal ion coordination and disassembled by reducing agents, and displays excellent chemical and thermal stability.

Author(s): Anil Desireddy [sup.1] , Brian E. Conn [sup.1] , Jingshu Guo [sup.1] , Bokwon Yoon [sup.2] , Robert N. Barnett [sup.2] , Bradley M. Monahan [sup.1] , Kristin Kirschbaum [...], Silver nanoparticles are susceptible to oxidation and have accordingly received less attention than gold nanoparticles; ultrastable silver nanoparticles are now reported, which can be produced in very large quantities as a single-sized molecular product, and the origins of their enhanced stability are elucidated using a single-crystal X-ray structure and first-principles calculations. Silver nanoparticles as good as gold Noble metals in nanoparticulate form find practical application as catalysts and in optoelectronics, energy conservation and many other fields. Gold nanoparticles, stable and easy to use, have proved much more useful and so have been studied more extensively than silver nanoparticles, which tend to be susceptible to oxidation. Anil Desireddy et al. describe a simple recipe for the large-scale production of single-sized silver nanoclusters, whose electronic structure gives them exceptional chemical stability. With the availability of stable silver nanoparticles, the metal's desirable electrical and physical properties, abundance and comparatively low cost could be harnessed in a wealth of new applications. Noble-metal nanoparticles have had a substantial impact across a diverse range of fields, including catalysis.sup.1, sensing.sup.2, photochemistry.sup.3, optoelectronics.sup.4,5, energy conversion.sup.6 and medicine.sup.7. Although silver has very desirable physical properties, good relative abundance and low cost, gold nanoparticles have been widely favoured owing to their proved stability and ease of use. Unlike gold, silver is notorious for its susceptibility to oxidation (tarnishing), which has limited the development of important silver-based nanomaterials. Despite two decades of synthetic efforts, silver nanoparticles that are inert or have long-term stability remain unrealized. Here we report a simple synthetic protocol for producing ultrastable silver nanoparticles, yielding a single-sized molecular product in very large quantities with quantitative yield and without the need for size sorting. The stability, purity and yield are substantially better than those for other metal nanoparticles, including gold, owing to an effective stabilization mechanism. The particular size and stoichiometry of the product were found to be insensitive to variations in synthesis parameters. The chemical stability and structural, electronic and optical properties can be understood using first-principles electronic structure theory based on an experimental single-crystal X-ray structure. Although several structures have been determined for protected gold nanoclusters.sup.8,9,10,11,12, none has been reported so far for silver nanoparticles. The total structure of a thiolate-protected silver nanocluster reported here uncovers the unique structure of the silver thiolate protecting layer, consisting of Ag.sub.2S.sub.5 capping structures. The outstanding stability of the nanoparticle is attributed to a closed-shell 18-electron configuration with a large energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, an ultrastable 32-silver-atom excavated-dodecahedral.sup.13 core consisting of a hollow 12-silver-atom icosahedron encapsulated by a 20-silver-atom dodecahedron, and the choice of protective coordinating ligands. The straightforward synthesis of large quantities of pure molecular product promises to make this class of materials widely available for further research and technology development.sup.14,15,16,17,18.

Silver thiolate clusters with an aromatic ligand shell and a core diameter of ~1.2 nm have been discovered only recently (19). Electrospray-ionization mass spectrometry (ESI-MS) identified these as discrete molecular [...], Noble-metal nanoparticles have had a substantial impact across a diverse range of fields, including catalysis (1), sensing (2), photochemistry (3), optoelectronics (4,5), energy conversion (6) and medicine (7). Although silver has very desirable physical properties, good relative abundance and low cost, gold nanoparticles have been widely favoured owing to their proved stability and ease of use. Unlike gold, silver is notorious for its susceptibility to oxidation (tarnishing), which has limited the development of important silver-based nanomaterials. Despite two decades of synthetic efforts, silver nanoparticles that are inert or have long-term stability remain unrealized. Here we report a simple synthetic protocol for producing ultrastable silver nanoparticles, yielding a single-sized molecular product in very large quantities with quantitative yield and without the need for size sorting. The stability, purity and yield are substantially better than those for other metal nanoparticles, including gold, owing to an effective stabilization mechanism. The particular size and stoichiometry of the product were found to be insensitive to variations in synthesis parameters. The chemical stability and structural, electronic and optical properties can be understood using first-principles electronic structure theory based on an experimental single-crystal X-ray structure. Although several structures have been determined for protected gold nanoclusters (8-12), none has been reported so far for silver nanoparticles. The total structure of a thiolate-protected silver nanocluster reported here uncovers the unique structure of the silver thiolate protecting layer, consisting of [Ag.sub.2][S.sub.5] capping structures. The outstanding stability of the nanoparticle is attributed to a closed-shell 18-electron configuration with a large energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, an ultrastable 32-silver-atom excavated-dodecahedral (13) core consisting of a hollow 12-silver-atom icosahedron encapsulated by a 20-silver-atom dodecahedron, and the choice of protective coordinating ligands. The straightforward synthesis of large quantities of pure molecular product promises to make this class of materials widely available for further research and technology development (14-18).

A large collection of non-overlapping solid objects (particles) in d-dimensional Euclidean space [[??].sup.d] is called a packing. The packing density φ is defined as the fraction of space [[??].sup.d] covered [...], Dense particle packings have served as useful models of the structures of liquid, glassy and crystalline states of matter (1-4), granular media (3,5), heterogeneous materials (3) and biological systems (6-8). Probing the symmetries and other mathematical properties of the densest packings is a problem of interest in discrete geometry and number theory (9,11). Previous work has focused mainly on spherical particles--very little is known about dense polyhedral packings. Here we formulate the generation of dense packings of polyhedra as an optimization problem, using an adaptive fundamental cell subject to periodic boundary conditions (we term this the 'adaptive shrinking cell' scheme). Using a variety of multi-particle initial configurations, we find the densest known packings of the four non-tiling Platonic solids (the tetrahedron, octahedron, dodecahedron and icosahedron) in three-dimensional Euclidean space. The densities are 0.782..., 0.947..., 0.904... and 0.836..., respectively. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other non-tiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. Combining our simulation results with derived rigorous upper bounds and theoretical arguments leads us to the conjecture that the densest packings of the Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This is the analogue of Kepler's sphere conjecture for these solids.

E-books promise to become a widespread delivery mechanism for educational resources. However, current e-books do not take full advantage of the power of computing tools. In particular, interaction with the […]

Chemists continually face a challenge of controlling chemical reactions or creating conditions that promote desirable reactions and limit undesirable ones. Researchers at New York University (NYU) developed a method to [...]