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This note highlights the recent finding of a previously unknown Roman villa with evidence for ‘watery’ deposits and subsequent early medieval activity.

This note highlights the recent finding of a previously unknown Roman villa with evidence for 'watery' deposits and subsequent early medieval activity. [ABSTRACT FROM AUTHOR]

Lithium (Li) metal is considered a hopeful anode for next-generation Li-ion batteries thanks to its ultra-high theoretical specific capacity, extra-low theoretical density, and low negative potential. However, the uncontrolled growth of Li dendrites and volume fluctuation during plating/stripping processes severely hamper its commercial application. Herein, ZnS seeds sealed in N, P, S co-doped carbon hollow rhombic dodecahedra (ZnS@NPS-C HRD) is fabricated as a superlithiophilic host for Li metal anodes (LMAs) to solve the above problems. In addition, the Li nucleation and deposition mechanism on ZnS@NPS-C HRD is investigated by in situ optical microscopy, ex-situ X-ray diffraction, scanning electron microscopy, and theoretical calculations. Owing to the synergistic strategy of ZnS seeds-inducing nucleation and Li-limited growth, the as-prepared composite exhibits stability for 300 cycles in asymmetric cells and a long lifespan over 1100 h in symmetric cells. Moreover, the ZnS@NPS-C HRD@Li|LiFePO 4 full cell demonstrates a reversible capacity of 100.91 mAh g -1 after 400 cycles at 1 C., (© 2024 Wiley‐VCH GmbH.)

A stable hollow Au20Si12 cage with Ih symmetry has been predicted using first-principles density functional theory. The stability of the cage-like Au20Si12 structure is verified by vibrational frequency analysis and molecular dynamics simulations. A relatively large highest occupied molecular orbitallowest unoccupied molecular orbital gap of 1.057 eV is found. Electronic structure analysis shows that clearly p-d hybridizations between Si atoms and Au atoms are of great importance for the stability of Au20Si12 cage. The cage-like Au20Si12 structure may have potential applications in semiconductor industry and microelectronics. [ABSTRACT FROM AUTHOR]

Despite the synthesis and structural characterization of closo‐hydroborate dianions, [BnHn]2− (n=6–12) more than 50 years ago, some ambiguity remains about the structure of [B8H8]2−. Although the solid‐state structure of [B8H8]2− was established by single‐crystal X‐ray studies in 1969, fast rearrangements in solution at accessible temperatures prevented its detailed characterization. We therefore stabilized a derivative of [B8H8]2− by using Cp2MBH3 and structurally characterized two new octaborane analogues, [(Cp2MBH3)2B8H6] (Cp=η5‐C5H5; M=Zr (1‐Zr) and Hf (1‐Hf)), so that the dynamics of the B8 skeleton were arrested. The solid‐state structures of both 1‐Zr and 1‐Hf comprise a dodecahedron core protected by {Cp2MBH3} moieties on both sides of the cluster. Spectroscopic characterization (11B NMR) validates the intactness of the B8 dodecahedron core in solution as well. Theoretical calculations establish that the two exo‐{Cp2MBH3} fragments provide structural and electronic structural stability to the B8 core and its intact dodecahedral dianionic nature. Furthermore, we propose isodesmic equations for the formation of higher analogues of the Bn core (n>8) guarded by different group 4 transition metals. Our analysis suggests that, as we move to higher polyhedra (n>10), the formation becomes unfavourable irrespective of metal. [ABSTRACT FROM AUTHOR]

In this study, a kind of graphene oxide-cuprous oxide (GO-Cu2O) nanocomposites was fabricated with different morphologies to serve as a photocatalytic material for the degradation of organic/inorganic dyes under visible light and the bactericidal effect against pathogenic bacteria. The GO-Cu2O was prepared with solid cube and hollow dodecahedra morphologies through in-situ synthesis, and characterized by scanning electron microscopy (SEM), transmission electron microscope (TEM), X-ray diffraction (XRD), Raman, Ultraviolet and visible spectrophotometry (UV/vis), and Fourier transform infrared spectroscopy. In comparison with cubic GO-Cu2O, the absorption and degradation efficiency of the GO-Cu2O dodecahedra (GCD) composite in Methyl orange (MO), Rhodamine B (RhB), and phenol was higher owning to the more active sites for the simultaneous dye and light absorption of hollow structure. The antibacterial effect of the GO-Cu2O dodecahedra was examined by the flat colony counting method with an excellent bactericidal effect against pathogenic bacteria. The possible mechanism for the preparation of GCD possessing the enhancement of the visible-light photocatalytic and antibacterial efficiencies were also investigated.

Nickel-cobalt (Ni-Co) oxide nanocages were synthesized by etching the cobalt-based metal-organic framework (Co-MOF) with nickel nitrate in an isopropyl alcohol solution. The dodecahedral Co-MOF (300 nm in size) was composed of micropores, while the Ni-Co oxide nanocages gained additional mesopores and macropores. Both Co-MOF and Ni-Co oxide electrodes in KOH behaved more like the nondiffusion-controlled pseudocapacitor through the surface adsorption/desorption with a concomitant faradaic charge-transfer reaction. In the presence of ferrocyanide/ferricyanide redox electrolyte, both nondiffusion- and diffusion-controlled currents contributed equally to the current response of Ni-Co oxide electrode at lower scan rates. Nondiffusion-limited processes governed the charge-storage behavior of Ni-Co oxide electrode at faster scan rates. The Ni-Co oxide electrode with redox electrolyte showed high specific capacities of 810 and 496 C g−1 at the charge/discharge current densities of 10 and 50 A g−1, respectively, much greater than that electrode without redox electrolyte (384 and 348 C g−1). Ni-Co oxide electrode with highly porous nanocages could provide large electrolyte/electrode interface to store more charges and short pathways to expedite the transport of electron and ion, showing a noticeable increase in its electrochemical performance compared with Co-MOF electrode. • Cobalt-based MOF acts as a template for the formation of Ni-Co oxide nanocages. • Ni-Co oxide nanocages gain additional mesopores and macropores for charge storage. • Nanocages provide short pathways to expedite the transport of electron and ion. • The specific capacity of Ni-Co oxide electrode is increased with redox electrolyte. [ABSTRACT FROM AUTHOR]

Abstract The cobalt nanoparticles (10 nm) were homogeneously embedded in the porous carbon dodecahedra (about 1 μm in size) through thermal pyrolysis of the ZIF-67 (zeolitic imidazolate framework-67) dodecahedra under an inert atmosphere. The pore sizes of the carbon dodecahedra were found to disperse in three ranges of micropores, small, and large mesopores. Cyclic voltammetry measurements indicated that the porous carbon-cobalt electrode with small particle size (SPC-Co) exhibited better electrocatalytic performance than that with large particle size (LPC-Co), primarily owing to its larger electrocatalytic surface for boosting the redox reaction between iodide and triiodide ions. Dye-sensitized solar cell (DSSC) using the SPC-Co counter electrode (CE) showed a superior photovoltaic conversion efficiency of 10.6%, which was better than those achieved by means of Pt (9.8%) and LPC-Co (9.0%) CEs. The improved photovoltaic behavior of DSSC employing the SPC-Co CE could be attributed to its lower internal resistance than the other CEs. The porous carbon rhombic dodecahedra with embedded cobalt nanoparticles could achieve fast kinetics and high electroactivity in catalyzing the iodide/triiodide redox couple. Graphical abstract Image 1 Highlights • Cobalt nanoparticles are well-distributed in the porous carbon rhombic dodecahedra. • The carbon dodecahedra with different pore sizes provide high electroactivity. • Caron dodecahedron catalyst boosts redox reaction between iodide and triiodide ions. • Dye-sensitized solar cell shows a high photovoltaic conversion efficiency of 10.6%. [ABSTRACT FROM AUTHOR]

Precisely carving of multi‐shelled manganese–cobalt oxide hollow dodecahedra (Co/Mn‐HD) with shell number up to three is achieved by a controlled calcination of the Mn‐doped zeolitic imidazolate framework ZIF‐67 precursor (Co/Mn‐ZIF). The unique multi‐shelled and polycrystalline structure not only provides a very large electrochemically active surface area (EASA), but also enhances the structural stability of the material. The residual C and N in the final structures might aid stability and increase their conductivity. When used in alkaline rechargeable battery, the triple‐shelled Co/Mn‐HD exhibits high electrochemical performance, reversible capacity (331.94 mAh g−1 at 1 Ag−1), rate performance (88 % of the capacity can be retained with a 20‐fold increase in current density), and cycling stability (96 % retention over 2000 cycles). [ABSTRACT FROM AUTHOR]

Graphical abstract Nb 2 Si 20 − anion has an irregular Nb 2 -doped endohedral structure, whereas Nb 2 Si 20 neutral adopts C 2h symmetric elongated dodecahedron cage structure. Interestingly, Nb 2 Si 20 −/0 exhibit significant aromaticity. Highlights • Nb 2 Si 20 neutral adopts C 2h symmetric elongated dodecahedron cage structure. • The Nb–Nb interactions in Nb 2 Si 20 −/0 are strong. • Nb 2 Si 20 −/0 exhibit significant aromaticity. Abstract We present a theoretical investigation on the geometric structures and bonding properties of Nb 2 Si 20 −/0 clusters using density functional theory calculations. The results showed that Nb 2 Si 20 − anion has an irregular Nb 2 -doped endohedral structure, whereas Nb 2 Si 20 neutral adopts C 2h symmetric elongated dodecahedron cage structure, which is composed of twelve pentagonal faces. Bond length, Wiberg bond order, constant electronic charge density, and molecular orbital analyses suggest that the Nb–Nb interactions in Nb 2 Si 20 −/0 are strong. Interestingly, Nb 2 Si 20 −/0 exhibit significant 3D aromaticity. [ABSTRACT FROM AUTHOR]

A new modified rhombic dodecahedron lattice structure is proposed by redefining the cross section of the struts of the original one with a shape parameter, and the detailed design method of the proposed lattice structure is also provided. For verification, some representative configurations of the proposed lattice structure were 3D-printed via Selective Laser Melting (SLM) with the material 316 L stainless steel. Quasi-static compression test of the fabricated samples was conducted. Finite element model was also established to investigate the mechanical properties of all the as-designed configurations. Finite element results are in good agreement with the experiment results. Compared with the original lattice structure, the proposed one exhibited better mechanical properties and energy absorption. In addition, the effects of the shape parameter on the deformation mode and the mechanical properties of the rhombic dodecahedron (RD) lattice structures were also discussed, while an optimal shape parameter of the proposed RD lattice structure is obtained. [ABSTRACT FROM AUTHOR]

Purpose: In brain imaging, the spherical PET system achieves the highest sensitivity when the solid angle is concerned. However, it is not practical. In this work, we designed an alternative sphere‐like scanner, the dodecahedral scanner, which has a high sensitivity in imaging and a high feasibility to manufacture. We simulated this system and compared the performance with a few other dedicated brain PET systems. Methods: Monte Carlo simulations were conducted to generate data of the dedicated brain PET system with the dodecahedral geometry (11 regular pentagon detectors). The data were then reconstructed using the in‐house developed software with the fully three‐dimensional maximum‐likelihood expectation maximization (3D‐MLEM) algorithm. Results: Results show that the proposed system has a high‐sensitivity distribution for the whole field of view (FOV). With a depth‐of‐interaction (DOI) resolution around 6.67 mm, the proposed system achieves the spatial resolution of 1.98 mm. Our simulation study also shows that the proposed system improves the image contrast and reduces noise compared with a few other dedicated brain PET systems. Finally, simulations with the Hoffman phantom show the potential application of the proposed system in clinical applications. Conclusions: In conclusion, the proposed dodecahedral PET system is potential for widespread applications in high‐sensitivity, high‐resolution PET imaging, to lower the injected dose. [ABSTRACT FROM AUTHOR]

We say that a polytope has the Rupert property if we can make a hole large enough in to permit another copy of to pass through. In this article, we show that among the 13 Archimedean solids, 8 have this property, namely, the cuboctahedron, the truncated octahedron, the truncated cube, the rhombicuboctahedron, the icosidodecahedron, the truncated cuboctahedron, the truncated icosahedron, and the truncated dodecahedron. [ABSTRACT FROM AUTHOR]

In the present work, porous Co 3 O 4 was easily prepared via thermal decomposition of metal-organic frameworks (MOFs). TG, FT-IR, XRD, SEM, TEM and N 2 adsorption-desorption were employed for characterizing the synthesized products. Based on cataluminescence (CTL) transduction principle, three MOFs including dodecahedra ZIF-67, nanosheets packed Co-MOF-71, nanoplate Co-BTC, and their corresponding derivatives Co 3 O 4 were used as sensing materials for H 2 S detection, respectively. The dodecahedra ZIF-67-derived dodecahedra Co 3 O 4 with high specific surface and exposed {110} lattice planes presented superior strong CTL property, and had a good linear relation in the concentration range of 3.3–27.5 μg L −1 with the detection limit of 1 μg L −1 (S/N = 3), while the original MOFs displayed no CTL signal. Eighteen common volatile organic compounds (VOCs) were investigated as possible interference, and the results indicated that MOFs-derived porous dodecahedra Co 3 O 4 would be one of excellent sensing material candidates for monitoring H 2 S with a promising application in routine analysis. [ABSTRACT FROM AUTHOR]

In this paper, two methods for softening the directivity balloon of dodecahedron loudspeakers when used for insulation measurements in buildings were proposed and evaluated. These proposals can be useful because the dodecahedron loudspeakers do not meet the uniformity requirements of the current Standards about noise insulation of façades in buildings. The radiation patterns of commercial dodecahedrons are highly uneven above 1 kHz and produced low coverage uniformity on the façade, as required by the Standard ISO 16283–3 in acoustic insulation measurements in buildings. This study aimed to validate the use of the proposed procedures on polyhedron-type loudspeakers in accordance with the latest ISO Standard. The first proposed method recommends addition of a reflecting surface at the back of the loudspeaker to combine the main and the mirror sources for smoothing the high-frequency directivity balloon of the setup. The second method required averaging of the dodecahedron emission from different angular positions on the façade and receiving room. This method is equivalent to averaging the directivity balloon of the dodecahedron loudspeaker. The two proposed methods were tested in the paper initially by computer simulation. First, the model of a real dodecahedron loudspeaker was generated using a commercial software. Next, different smoothing proposals were applied to the dodecahedron model to generate several secondary sound sources, one for each variant of the methods. All these new sound sources were analysed with an author’s software on a replica of the ISO Standard scenario by calculating the maximum horizontal dimension of façades with different shapes that verifies the criterions of the Standard. Finally, all of the proposals were categorized and sorted according to the façade size to cover uniformly, and some suggestions were made on optimal strategies to smooth the dodecahedron coverage. As a final point, some actual measurements of the best proposed setups have been implemented. [ABSTRACT FROM AUTHOR]

Many properties of solid foams depend on the distribution of the pore sizes and their organization in space. However, these two parameters are very difficult to control with most traditional foaming techniques. Here we show how microfluidics can be used to tune the polydispersity of the foams (mono- vs different polydispersities) and the spatial organization of the pores (ordered vs disordered). For this purpose, the microfluidic flow-focusing technique was modified such that the gas pressure oscillates periodically, which translates into periodically oscillating bubble sizes in the liquid foam template. The liquid foams were generated from chitosan solutions and then gelled via cross-linking with genipin before we freeze-dried them to obtain a solid foam with a specific structure. The study at hand fills two existing scientific gaps. On the one hand, we present a novel approach for the generation of foams with controlled polydispersity. On the other hand, we obtained a solid foam with a new structure for foam templating consisting of rhombic dodecahedra. The controlled variation of the foam’s structure will allow studying systematically structure–property relations. Moreover, being fully biobased, this type of solid foam is a suitable candidate for applications in tissue engineering. [ABSTRACT FROM AUTHOR]

Dodecahedral SmVO 4 nanocrystals with uniform size had been successfully synthesized by a facile hydrothermal process in the presence of potassium hydroxide and urea. The dodecahedron-like SmVO 4 was characterized by X-ray diffraction, field-emission scanning electron microscopy, Fourier transform infrared, X-Ray photoelectron spectroscopy, high-resolution transmission electron microscopy and photoluminescence. The possible growth mechanism of the SmVO 4 nanocrystals with dodecahedral shape was discussed. Under excitation at 315 nm, the SmVO 4 sample exhibits strong orange emission while it as the host doped with suitable amount of Eu 3+ ions shows strong reddish orange emission. The diversity in emission intensity detected from SmVO 4 : x% Eu 3+ (x = 1, 3, 5, 7) was compared. The hydrothermal method for preparing dodecahedral SmVO 4 nanocrystals provides us an idea to synthesize other rare earth orthovanadate nanomaterials with special morphology and interesting optical property. [ABSTRACT FROM AUTHOR]

Viewing fullerenes as plane graphs with facial cycles being pentagonal and hexagonal only, it is shown how to reduce an arbitrary fullerene to the (graph of the) dodecahedron. This can be achieved by a sequence of eight reduction steps, seven of which are local operations and the remaining reduction step acts globally. In any case, the resulting algorithm has polynomial running time. [ABSTRACT FROM AUTHOR]

In this work, we demonstrate that the electrocatalytic activity of transition metal chalcogenides can be greatly enhanced by simultaneously engineering the active sites, surface area, and conductivity. Using metal-organic frameworks-derived (Ni,Co)Se 2 /C hollow rhombic dodecahedra (HRD) as a demonstration, we show that the incorporation of Ni into CoSe 2 could generates additional active sites, the hierarchical hollow structure promotes the electrolyte diffusion, the in-situ hybridization with C improves the conductivity. As a result, the (Ni,Co)Se 2 /C HRD exhibit superior performance toward the overall water-splitting electrocatalysis in 1 M KOH with a cell voltage as low as 1.58 V at the current density of 10 mA cm −2 , making the (Ni,Co)Se 2 /C HRD as a promising alternative to noble metal catalysts for water splitting. [ABSTRACT FROM AUTHOR]

BiVO 4 , an excellent photocatalyst for oxygen production, has been studied extensively. Many attempts have been made to change the conduction band of BiVO 4 to satisfy the H 2 O/H 2 potential. In this paper, yttrium is introduced to adjust the energy band structure of BiVO 4 . A novel BiVO 4 :YVO 4 solid solution with a new dodecahedron shape exposing two facets, {1 0 1} and {1 0 0}, is successfully prepared. On doping with Y, the crystal system of BiVO 4 changes from monoclinic to tetragonal. The improved symmetry of the crystal system makes the (1 0 0) and (0 1 0) of {1 0 0} facets entirely identical, resulting in dodecahedron tetragonal Bi x Y 1− x VO 4 . The energy levels of the two facets show slight nonconformity. So the photogenerated electrons and holes can be separated efficiently between the adjacent exposed facets to produce H 2 and O 2 , respectively. Through the study of photocatalytic performance, Bi x Y 1− x VO 4 with Pt as co-catalyst shows highly efficient photocatalytic activity and can split pure water at the stoichiometric ratio. [ABSTRACT FROM AUTHOR]

A new clathrate type has been discovered in the Ba/Cu/Zn/P system. The crystal structure of the Ba8 M24P28+ δ ( M=Cu/Zn) clathrate is composed of the pentagonal dodecahedra common to clathrates along with a unique 22-vertex polyhedron with two hexagonal faces capped by additional partially occupied phosphorus sites. This is the first example of a clathrate compound where the framework atoms are not in tetrahedral or trigonal-pyramidal coordination. In Ba8 M24P28+ δ a majority of the framework atoms are five- and six-coordinated, a feature more common to electron-rich intermetallics. The crystal structure of this new clathrate was determined by a combination of X-ray and neutron diffraction and was confirmed with solid-state 31P NMR spectroscopy. Based on chemical bonding analysis, the driving force for the formation of this new clathrate is the excess of electrons generated by a high concentration of Zn atoms in the framework. The rattling of guest atoms in the large cages results in a very low thermal conductivity, a unique feature of the clathrate family of compounds. [ABSTRACT FROM AUTHOR]

An appendix is presented of regular dodecahedra with topics including eigenvalues of operators, the positive direction of Onsager's conjecture, and simplifications.

A bilaterally symmetrical convex dodecahedron consisting of twelve quadrilateral faces is derived from the icosahedron via a process akin to Fuller’s Jitterbug Transformation. The unusual zygomorphic dodecahedron so obtained is shown to harbor a bilaterally symmetrical jazz/blues harmonic code on its twelve faces that is related to such fundamental music theoretical constructs as the Circle of Fifths and Euler’s tonnetz. Curiously, the patterning within the aforementioned zygo-dodecahedron is discernibly similar to that observed in a ventral view of the human brain. Moreover, this same pattern is arguably evident during development of the embryonic pharynx. A possible role for the featured zygo-dodecahedron in cephalogenesis is considered. Recent studies concerning type II cadherins, an important class of proteins that promote cell adhesion, have generated data that is demonstrated to conform to this zygo-dodecahedral brain model in a substantially congruous manner.

Earth abundant element clathrate phases are of interest for a number of applications ranging from photovoltaics to thermoelectrics. Silicon-containing type I clathrate is a framework structure with the stoichiometry A8-xSi46 (A = guest atom such as alkali metal) that can be tuned by alloying and doping with other elements. The type I clathrate framework can be described as being composed of two types of polyhedral cages made up of tetrahedrally coordinated Si: pentagonal dodecahedra with 20 atoms and tetrakaidecahedra with 24 atoms in the ratio of 2:6. The cation sites, A, are found in the center of each polyhedral cage. This review focuses on the newest discoveries in the group 13-silicon type I clathrate family: A8E8Si38 (A = alkali metal; E = Al, Ga) and their properties. Possible approaches to new phases based on earth abundant elements and their potential applications will be discussed. [ABSTRACT FROM AUTHOR]

This study examines the facet-dependent optical properties of size-tunable Ag-Cu2O core-shell nanocrystals with 38, 42, and 50 nm cubic Ag cores. The Ag cores were prepared from octahedral Au seeds. The Cu2O shells are single-crystalline. In the case of Au@Ag-Cu2O nanocrystals with 42 nm Ag cores, the Ag surface plasmon resonance (SPR) absorption band at 485 nm has been widely red-shifted to 730, 755, and 775 nm for rhombic dodecahedra, truncated octahedra, and cuboctahedra, respectively, after forming the Cu2O shells. The Ag SPR band positions are mostly fixed despite large changes in the shell thickness, showing the presence of facet-dependent optical properties. Because of the strong Ag SPR band absorption, all samples exhibit a better photothermal activity than that of Au-Cu2O nanocrystals. Facet-dependent heat transmission may be present for particles with a Ag SPR band much deviated from the laser wavelength, but this phenomenon is lost for particles with an SPR band approaching the excitation wavelength as the particles become highly photothermally efficient to give solution temperatures of 80-95 °C within 3 min of laser irradiation. [ABSTRACT FROM AUTHOR]

Cobalt oxide hollow nanododecahedra (Co 3 O 4 -HND) is synthesized by a facile thermal transformation of cobalt-based metal-organic framework (Co-MOF, ZIF-67) template. The morphology and properties of the Co 3 O 4 -HND are characterized by a set of techniques, including transmission electron microscope (TEM), powder X-ray diffraction (XRD), scanning electron microscope (SEM) and Brunner–Emmet–Teller (BET). When tested as a non-enzymatic electrocatalyst for glucose oxidation reaction, the Co 3 O 4 -HND exhibits a high activity and shows an outstanding performance for determining glucose with a wide window of 2.0 μM to 6.06 mM, a high sensitivity of 708.4 μA mM −1 cm −2 , a low detection limit of 0.58 μM ( S / N =3), and fast response time(<2 s). Based on the nonenzymatic oxidation of glucose, Co 3 O 4 -HND could be served as an attractive non-enzyme and noble-metal-free electrocatalyst in glucose fuel cell (GFC) due to its excellent electrochemical properties, low cost and facile preparation. [ABSTRACT FROM AUTHOR]

Fundamental studies and practical use of metal nanoparticles (NPs) frequently depend on the ability to reproducibly synthesize large quantities of shape-specific NPs. For this reason, facile synthetic procedures are desired that will lead to large quantities of uniformly sized metal NPs exhibiting specific shapes. Here, we report a general approach to the large-scale synthesis of noble metal nanocrystals having well-defined shapes and a narrow size distribution. This method utilizes seed-mediated NP growth in aqueous suspensions of cationic surfactants and metal salts. It leads to a ~60-fold increase in NP volumetric production capacity, compared to the most widely used solution-based synthetic methods. In addition, it uses up to 100 times less cationic surfactant than conventional solution-based methods. The applicability of the method is demonstrated in the synthesis of Pd nanocubes, rhombic dodecahedra, and polyhedrons with low index facets; branched Pd nanocrystals; alloy Pt/Pd nanocubes; Ag nanocubes. The advantages and limitations of the approach are discussed, including accessible shapes, growth kinetics, and the capability to scale up the synthetic procedure. [ABSTRACT FROM AUTHOR]

We report the crystal structure of a novel 60-subunit dodecahedral cage that results from self-assembly of a re-engineered version of a natural protein (PduA) from the Pdu microcompartment shell. Biophysical data illustrate the dependence of assembly on solution conditions, opening up new applications in microcompartment studies and nanotechnology. [ABSTRACT FROM AUTHOR]

Dense particle packing in a confining volume remains a rich, largely unexplored problem, despite applications in blood clotting, plasmonics, industrial packaging and transport, colloidal molecule design, and information storage. Here, we report densest found clusters of the Platonic solids in spherical confinement, for up to N =60 constituent polyhedral particles. We examine the interplay between anisotropic particle shape and isotropic 3D confinement. Densest clusters exhibit a wide variety of symmetry point groups and form in up to three layers at higher N. For many N values, icosahedra and dodecahedra form clusters that resemble sphere clusters. These common structures are layers of optimal spherical codes in most cases, a surprising fact given the significant faceting of the icosahedron and dodecahedron. We also investigate cluster density as a function of N for each particle shape. We find that, in contrast to what happens in bulk, polyhedra often pack less densely than spheres. We also find especially dense clusters at so-called magic numbers of constituent particles. Our results showcase the structural diversity and experimental utility of families of solutions to the packing in confinement problem. [ABSTRACT FROM AUTHOR]

A closed connected hyperbolic n-manifold bounds geometrically if it is isometric to the geodesic boundary of a compact hyperbolic (n +1)-manifold. A. Reid and D. Long have shown by arithmetic methods the existence of infinitely many manifolds that bound geometrically in every dimension. We construct here infinitely many explicit examples in dimension n = 3 using right-angled dodecahedra and 120-cells and a simple colouring technique introduced by M. Davis and T. Januszkiewicz. Namely, for every k ≥ 1, we build an orientable compact closed 3-manifold tessellated by 16k right-angled dodecahedra that bounds a 4-manifold tessellated by 32k right-angled 120-cells. A notable feature of this family is that the ratio between the volumes of the 4-manifolds and their boundary components is constant and, in particular, bounded. [ABSTRACT FROM AUTHOR]

Stoichiometric control of Ru, Ag, and tetrazolyl ligands resulted in the formation of different heterometallic Ru--Ag supramolecular architectures. Although the reaction of Ru and 5-(2-hydroxyphenyl)-1H-tetrazolyl (LH2) in a molar ratio of 2:1 or 6:4 resulted in the formation of dimeric or hexameric Ru complexes, Ag metal ions caused the Ru complexes to form threedimensional cylindrical Ru6Ag6L6 and double-cone-shaped Ru6Ag8L6 complexes by occupying vacant coordination sites. [ABSTRACT FROM AUTHOR]

Silicon analogues of the most prominent carbon nanostructures, namely, hollow spheroidals such as C60 and the fullerene family, have been unknown to date. Herein we show that discrete Si20 dodecahedra, stabilized by an endohedral guest and valence saturation, are accessible in preparative yields through a chloride-induced disproportionation reaction of hexachlorodisilane in the presence of tri( n-butyl)amine. X-ray crystallography revealed that each silicon dodecahedron contains an endohedral chloride ion that imparts a net negative charge. Eight chloro substituents and twelve trichlorosilyl groups are attached to the surface of each cluster in a strictly regioregular arrangement, a thermodynamically preferred substitution pattern according to quantum-chemical assessment. Our results demonstrate that the wet-chemical self-assembly of a complex, monodisperse Si nanostructure is possible under mild conditions starting from simple Si2 building blocks. [ABSTRACT FROM AUTHOR]

The article presents various mathematical facts and derivations related to platonic gap between platonic solids including octahedra, icosahedra, and dodecahedra. Topics discussed include possibility of a perfectly closed loop of congruent regular tetrahedra, a regular tetrahedral structure is the spiral chain known as the tetrahelix and a theorem, the last tetrahedron in a Steinhaus chain cannot coincide with the first.

Presented here is a metastable metal–organic framework built from the alternating connection of dodecahedral and cubic cages. To enhance its sorption properties, three kinds of different activation treatments were performed to decrease the deleterious effect of solvent surface tension during activation processes. [ABSTRACT FROM AUTHOR]

The article looks at the use of differentiation in linking insides of geometric figures to their boundaries. Topics covered include the differentiation formulas for Platonic solids including the tetrahedron, the cube, and the dodecahedron, a theorem in evaluating the connection between the interior of the solids to their boundaries, and comparison between inradius and circumradius in Platonic solids.

Here we report a one-pot route for the synthesis of nickel dodecahedra with 52.3 ± 0.1 emu g-1 of saturation magnetization. The procedure is very simple, and only three chemicals (NiCl2.6H2O, isopropanol and polyvinylpyrrolidone) are used throughout the entire synthetic process. During the reaction, it is believed that the application of isopropanol and the amount of polyvinylpyrrolidone play an essential role in forming the dodecahedral morphology of the final product. Furthermore, a formation process of twinning and the influence of reaction kinetic factors were proposed to explain the formation of nickel dodecahedra. [ABSTRACT FROM AUTHOR]

Ultrathin crystalline nanosheets give an extremely high surface area of a specific crystal facet with unique physical and chemical properties compared with normal three-dimensionally polyhedral nanocrystals (NCs). However, the ultrathin metal nanosheets tend to curl themselves or assemble with each other sheet by sheet, which may reduce the effective surface area and accordingly the catalytic activity to a great extent. Here we report a facile wet-chemical route that allows the fabrication of novel excavated rhombic dodecahedral (ERD) PtCu3 alloy NCs with ultrathin nanosheets of high-energy {110} facets. The surface area was measured to be 77 m² g-1 by CO stripping, although the particle size is about 50 nm. Electrochemical characterizations showed that the ERD PtCu3 NCs exhibit excellent electrocatalytic performance and high antipoisoning activity in comparison with commercial Pt black andPtCu3 alloy NCs with {111} surfaces. [ABSTRACT FROM AUTHOR]

A new series of lanthanide complexes was synthesized, and the geometry and preliminary magnetic measurements of the complexes were explored. The specific ligand used (N'-(2-hydroxy-3-methoxybenzylidene)benzhydrazide) (H2hmb) was synthesized using a Schiff-base approach and was employed due to the presence of a coordination pocket that is able to accommodate magnetically selective lanthanide ions. The series can be divided into two groups that are categorized by a drastic structural rearrangement. The first group, Type I, contains six analogous complexes with the formula [MIII2(Hhmb)3(NCS)3]·2MeOH·py (M = Y 1, Eu 2, Gd 3, Tb 4, Dy 5, Ho 6), while the second group, Type II, contains two dinuclear complexes with formula [MIII2(Hhmb)2(NCS)4(MeOH)2] (M = Er 7, and Yb 8). Single-crystal X-ray analysis revealed that all MIII ions in Type I exhibit monocapped distorted square antiprismatic geometries, while those of Type II exhibit distorted dodecahedron geometry. The direct current and alternating current magnetic measurements were carried out on all complexes, with 5, 7, and 8 exhibiting slow relaxation of the magnetization under an applied optimum dc field. Furthermore, complex 8 is the first example of a dinuclear Yb-based single-molecule magnet showing field-dependent multiple relaxation processes. [ABSTRACT FROM AUTHOR]

The nucleation kinetics of the rotator phase in hard cuboctahedra, truncated octahedra, and rhombic dodecahedra is simulated via a combination of forward flux sampling and umbrella sampling. For comparable degrees of supersaturation, the polyhedra are found to have significantly lower free-energy barriers and faster nucleation rates than hard spheres. This difference primarily stems from localized orientational ordering, which steers polyhedral particles to pack more efficiently. Orientational order hence fosters here the growth of orientationally disordered nuclei. [ABSTRACT FROM AUTHOR]

The Eyring/Sabine equations assume that in a large irregular room a sound wave travels in straight lines from one surface to another, that the surfaces have an average sound absorption coefficient αav, and that the mean-free-path between reflections is 4 V/Stot where V is the volume of the room and Stot is the total area of all of its surfaces. No account is taken of diffusivity of the surfaces. The 4 V/Stot relation was originally based on experimental determinations made by Knudsen (Architectural Acoustics, 1932, pp. 132-141). This paper sets out to test the 4 V/Stot relation experimentally for a wide variety of unoccupied concert and chamber music halls with seating capacities from 200 to 5000, using the measured sound strengths Gmid and reverberation times RT60,mid. Computer simulations of the sound fields for nine of these rooms (of varying shapes) were also made to determine the mean-free-paths by that method. The study shows that 4 V/Stot is an acceptable relation for mean-free-paths in the Sabine/Eyring equations except for halls of unusual shape. Also demonstrated is the proper method for calibrating the dodecahedral sound source used for measuring the sound strength G, i.e., the reverberation chamber method. [ABSTRACT FROM AUTHOR]

We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non-trivial topology: the Poincaré dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to a mixed problem posed on a fundamental domain determined by the quaternionic calculus. We adopt a variational approach using a space of finite elements that is invariant under the action of the binary icosahedral group. The computation of the transient waves is validated with their spectral analysis by computing a lot of eigenvalues of the Laplace–Beltrami operator. [ABSTRACT FROM AUTHOR]

By fusing Lu2O3 and TeO2 in a molar ratio of 1:3 in a CsCl flux, colorless single crystals of the lutetium(III) oxotellurate(IV) Lu2Te3O9 could be obtained as first representative of the structurally so far unknown C-type for the composition M2Te3O9. The title compound crystallizes triclinically in space group P $\bar{1}$ with a = 689.67(4) pm, b = 1320.91(8) pm, c = 1450.06(9) pm, α = 110.057(3)°, β = 90.606(3)°, γ = 100.125(3)°, and Z = 6. The crystal structure contains six different Lu3+ cations in eightfold (Lu1 and Lu2: trigonal dodecahedra) and sevenfold (Lu3 and Lu6: monocapped trigonal prisms; Lu4 and Lu5: pentagonal bipyramids) oxygen coordination. These lutetium-oxygen polyhedra ( d(Lu-O) = 214-274 pm) are condensed to serrated layers according to 2∞{[Lu6O26]34-} that are stacked along [100]. The oxotellurate(IV) partial structure consists of basically nine crystallographically independent [TeO3]2- ( d(Te-O) = 184-196 pm) units connecting the above-mentioned layers to a three-dimensional framework. Strong secondary Te4+ ···O2- interactions between adjacent [TeO3]2- entities as common feature in the crystal structures of all known ternary lanthanoid(III) oxotellurates(IV) are also present in the crystal structure of Lu2Te3O9. Depending upon the range of these secondary contacts taken into account, the [TeO3]2- units are linked to form one-dimensional strands ( d(Te ···O) = 237-272 pm) like in B-type Dy2Te3O9 or even two-dimensional layers emerge ( d(Te ···O) = 237-285 pm). [ABSTRACT FROM AUTHOR]

By fusing Lu2O3 and TeO2 in a molar ratio of 1:3 in a CsCl flux, colorless single crystals of the lutetium(III) oxotellurate(IV) Lu2Te3O9 could be obtained as first representative of the structurally so far unknown C-type for the composition M2Te3O9. The title compound crystallizes triclinically in space group P $\bar{1}$ with a = 689.67(4) pm, b = 1320.91(8) pm, c = 1450.06(9) pm, α = 110.057(3)°, β = 90.606(3)°, γ = 100.125(3)°, and Z = 6. The crystal structure contains six different Lu3+ cations in eightfold (Lu1 and Lu2: trigonal dodecahedra) and sevenfold (Lu3 and Lu6: monocapped trigonal prisms; Lu4 and Lu5: pentagonal bipyramids) oxygen coordination. These lutetium-oxygen polyhedra ( d(Lu-O) = 214-274 pm) are condensed to serrated layers according to 2∞{[Lu6O26]34-} that are stacked along [100]. The oxotellurate(IV) partial structure consists of basically nine crystallographically independent [TeO3]2- ( d(Te-O) = 184-196 pm) units connecting the above-mentioned layers to a three-dimensional framework. Strong secondary Te4+ ···O2- interactions between adjacent [TeO3]2- entities as common feature in the crystal structures of all known ternary lanthanoid(III) oxotellurates(IV) are also present in the crystal structure of Lu2Te3O9. Depending upon the range of these secondary contacts taken into account, the [TeO3]2- units are linked to form one-dimensional strands ( d(Te ···O) = 237-272 pm) like in B-type Dy2Te3O9 or even two-dimensional layers emerge ( d(Te ···O) = 237-285 pm). [ABSTRACT FROM AUTHOR]

Human adenovirus serotypes Ad3, Ad7, Ad11, and Ad14 use the epithelial junction protein desmoglein 2 (DSG2) as a receptor for infection. During Ad infection, the fiber and penton base capsid proteins are produced in vast excess and form hetero-oligomers, called pentons. It has been shown for Ad3 that pentons self-assemble into penton-dodecahedra (PtDd). Our previous studies with recombinant purified Ad3 PtDd (produced in insect cells) showed that PtDd bind to DSG2 and trigger intracellular signaling resulting in the transient opening of junctions between epithelial cells. So far, a definitive proof for a function of Ad3 PtDd in the viral life cycle is elusive. Based on the recently published 3D structure of recombinant Ad3 PtDd, we generated a penton base mutant Ad3 vector (mu-Ad3GFP). mu-Ad3GFP is identical to its wild-type counterpart (wt-Ad3GFP) in the efficiency of progeny virus production; however, it is disabled in the production of PtDd. For infection studies we used polarized epithelial cancer cells or cell spheroids. We showed that in wt-Ad3GFP infected cultures, PtDd were released from cells before viral cytolysis and triggered the restructuring of epithelial junctions. This in turn facilitated lateral viral spread of de novo produced virions. These events were nearly absent in mu-Ad3GFP infected cultures. Our in vitro findings were consolidated in mice carrying xenograft tumors derived from human epithelial cancer cells. Furthermore, we provide first evidence that PtDd are also formed by another DSG2-interacting Ad serotype, the newly emerged, highly pathogenic Ad14 strain (Ad14p1). The central finding of this study is that a subgroup of Ads has evolved to generate PtDd as a strategy to achieve penetration into and dissemination in epithelial tissues. Our findings are relevant for basic and applied virology, specifically for cancer virotherapy. [ABSTRACT FROM AUTHOR]

Surfactant-free Cu2O nanocrystals, including cubes exposing {100} crystal planes, octahedra exposing {111} crystal planes, and rhombic dodecahedra exposing {110} crystal planes, were used as model catalysts to study the effect of the crystal plane on the surface chemistry and catalytic performance for CO oxidation of Cu2O nanocrystals. The catalytic performance follows the order of octahedra≫rhombic dodecahedra>cubes; this suggests that Cu2O(111) is most active in catalyzing CO oxidation among Cu2O (111), (110), and (100) surfaces. CO temperature-programmed reduction results demonstrate that Cu2O octahedra are the most easily reduced of the Cu2O cubes, octahedra, and rhombic dodecahedra. Diffuse reflectance FTIR spectra show that CO chemisorption on Cu2O nanocrystals depends on their shape and the chemisorption temperature. CO chemisorption is strongest on rhombic dodecahedra at 30 °C, but at 150 °C on octahedra. Both the reducibility and chemisorption ability of various Cu2O nanocrystals toward CO are consistent with their catalytic performance in CO oxidation. The observed surface chemistry and catalytic performance in CO oxidation of various Cu2O nanocrystals can be well correlated with their exposed crystal plane and surface composition/structure. Cu2O octahedra expose the {111} crystal plane with coordinated, unsaturated CuI sites, and thus, are most active in chemisorbing CO and catalyzing CO oxidation. These results nicely demonstrate the crystal-plane-controlled surface chemistry and catalytic performance of oxide catalysts. [ABSTRACT FROM AUTHOR]

ZIF-derived N, S-codoped porous carbon dodecahedra are prepared and used as the high-performance cathode for aqueous ZHSC via a facile two-step doping strategy, which exhibit an ultra-long cycle life and a remarkable cycling stability with 97.1% capacity retention after 100,000 charge–discharge cycles (3960h). [Display omitted] • N, S-PCD were synthesized by a facile two-step doping strategy. • DFT reveals that N and S dopants effectively boost the chemical adsorption of Zn2+. • Ex-situ SEM, XRD and XPS are applied to explore the working mechanism of N, S-PCD. • The assembled Zn//N, S-PCD device exhibits a long cycle life for 100,000 cycles. Aqueous Zn-ion hybrid supercapacitors (ZHSCs) are promising energy storage devices for their intrinsic advantages of high theoretical capacity, low-cost, and intrinsic safety. However, due to the lack of efficient cathode materials for reversible insertion/extraction of Zn2+ ions, it remains a pivotal challenge to high cycling-stability ZHSCs. Herein, we report a facile two-step doping strategy to synthesize zeolitic imidazolate framework (ZIF)-derived N, S-codoped porous carbon dodecahedra (N, S-PCD), using as the high-performance cathode for ultralong-life aqueous ZHSC. Integrating the hierarchical porous architecture and N, S dual-doping, the as-assembled Zn//N, S-PCD ZHSC delivers a specific capacity of 133.4 mA h g−1 (300.2 F g−1) at 0.2 A g−1, and maximum energy density of 106.7 W h kg−1 at the power density of 160 W kg−1. Moreover, an ultra-long cycle life has been achieved with the device, retaining 97.1% capacity after 100,000 charge–discharge cycles (∼3960 h), which is the maximum life span for ZHSCs to date. Mechanism studies reveal that thes dual-doping of N and S could effectively boost the chemical adsorption of Zn2+ ions and improve the electronic conductivity, which synergistically enhance the Zn-ion storage performance. [ABSTRACT FROM AUTHOR]