Zigzag Motif Research Articles

Magnetocaloric effect in 1D-polymers bearing 15-metallacrown-5 {GdCu5}3+ units and anionic oxalate complexes.

Two complexes {[GdCu5(GlyHA)5(H2O)7Cr(C2O4)3]·11.02H2O}n (1) and {{[GdCu5(GlyHA)5(H2O)6]μ2-[Cu(C2O4)2(H2O)]}2μ4-[Cu(C2O4)2]·15.8H2O}n (2), were obtained as outcomes of the reactions between the cationic hexanuclear {GdCu5(GlyHA)5}3+ 15-metallacrown-5 complex (where GlyHA2- = glycinehydroxamate) and the anionic oxalate complexes K3[Cr(C2O4)3] or K2[Cu(C2O4)2]. Both 1 and 2 possess polymeric 1D-chain structures according to X-ray structural analysis. As a consequence of the geometric orientations of the donor atoms in the oxalates from [Cr(C2O4)3]3-, the Cu5 mean planes of neighboring 15-metallacrown-5 units {GdCu5(GlyHA)5}3+ are angled at 75.5° to each other, which leads to formation of a zig-zag motif in the 1D-chains of complex 1. The centrosymmetric complex 2 contains two structurally different bis(oxalato)cuprate anions μ2-[Cu(C2O4)2(H2O)]2-, for one of which, coordination to two adjacent {GdCu5(GlyHA)5}3+ units leads to formation of linear 1D-chains in 2, while the second type, μ4-[Cu(C2O4)2]2-, is coordinated to four {GdCu5(GlyHA)5}3+ units, causing the cross-linking of single 1D-chains into a double-chain 1D coordination polymer. Studies of χMT vs. T data for 1 and 2 in a 2-300 K temperature range revealed the presence of both ferromagnetic and antiferromagnetic interactions amongst paramagnetic centres. The experimental χMT vs. T data for 1 were fitted using a model which takes into account exchange interactions between adjacent copper(II) ions, the Gd-Cu exchange interactions within {GdCu5(GlyHA)5}3+ units and additionally Gd-Cr exchange interactions. Fitting of the χMT vs. T data for 2 was not possible, since coordination of μ4-[Cu(C2O4)2]2- to {GdCu5(GlyHA)5}3+ led to the non-equivalence of several Cu-Cu exchange interactions within the metallacrown units and hence a superfluity of fittable parameters. Complexes 1 and 2 are the first examples of 15-metallacrown-5 complexes demonstrating a magnetocaloric effect (-ΔSM at 13 T reaches 24.26 J K-1 kg-1 at 5 K and 19.14 J K-1 kg-1 at 4 K for 1 and 2, respectively).

Controlling and visualizing fracture of 2D crystals by wrinkling

Shaping two-dimensional (2D) crystals with well-defined edges along specific directions remains technically challenging due to the intrinsic lattice discreteness and anisotropy in their fracture toughness. The patterns of crystal cleavage are determined by the fracture resistance and loading conditions, and usually display kinking features. We show that the fracture of single-crystalline 2D films (MoS2, MoTe2, graphene) can be controlled by mechanically-induced wrinkles, and the distortion of their profiles can visualize the distorted local strain state near the crack tip. In thin samples with stretch-induced wrinkles, the elastic driving force with effective anisotropy steers crack propagation, resulting in straight edges following the corrugation profile. In contrast, thick samples remain flat under stretch for their elevated bending resistance, and the cracks advance with sawtooth patterns following the zigzag motif. The experimental findings are explained by wrinkling-induced elastic anisotropy, which dominates over fracture anisotropy. The control of fracture in 2D crystals can be applied to fabricate micro- and nanostructures for their applications in electromechanical and optoelectronic devices.

Techniques and Ideas. Zigzag Motif, Barbed Line, and Shaded Band in the Meso-Neolithic Bone Assemblage at Zamostje 2, Volga-Oka Region (Russia)

Abstract Mesolithic geometric ornamentation is a part of the complex worldview of the latest hunter-gatherer societies. Questions about the functional role of the ornament in utilitarian objects – knives, daggers, arrowheads, etc. – do not have an unambiguous answer. Despite a variability of ornamental motives used, there are some stable connections between certain types of ornaments with some categories of bone tools. On the materials of the Late and Final Mesolithic layers of the wetland site Zamostje 2 (Volga-Oka region), we will consider some examples with the zigzag motif, the most numerous and heterogeneous type of ornament, as well as rarely presented motives of “ladders” and “lines with dots or eyelashes.” The number of samples (120) is sufficient to draw some preliminary conclusions about the context of their application. So, the zigzag is observed on different types of tools, but its connection with sharp-piercing objects is most clearly manifested. The type of relief zigzag is inextricably related to slotted sickle-shaped tools. Zigzag is often the only decorative element on an item and is expressed by a simple or double line; less often it is included in complex compositions. Both types of zigzags and methods of application (fine engraving, scraping, relief carving, etc.) were not regulated and obviously performed different functions depending on the compositional characteristics and the raw material’s type. Compositions of “ladders” located at an angle to each other are also associated with projectile weapons. Lines “with eyelashes” appear to have been a part of the standard dagger decoration.

PERANCANGAN KAP LAMPU DEKORATIF BERBAHAN BIO LEATHER KACANG KEDELAI

Soybean shell waste contains organic material with pH levels classified as acidic which can endanger environmental sustainability and pollute water and soil. This research raises the issue of utilizing soybean shell waste into more useful products. Soybean shell waste is used as new materials in the form of composites to be used as products that have economic value and overcome negative environmental impacts. The composite results in this study in this study were in the form of soybean skin bio leather sheets which were then analyzed for raw material talent to determine the potential of soybean skin bio leather sheets to be used as alternative product design materials. The actions taken to identify the talent of the sheet are by exploring and testing the translucency of the light to determine the distribution of the light produced, testing the sustainable sheet with the process of soaking the soil and water, and giving color. After analyzing material talent, in product design using the MACAK design method in the design so that product recommendations are found using soybean skin bio leather material. One of the product recommendations that can be developed is the design of a decorative lampshade with a Scandinavian concept with a weaving technique with a zig zag motif and geometry for hanging wall lamps, and table lamps using soybean skin bio leather. The results of the product design of hanging decorative lampshades, table lamps

Enabling three-dimensional porous architectures via carbonyl functionalization and molecular-specific organic-SERS platforms

Molecular engineering via functionalization has been a great tool to tune noncovalent intermolecular interactions. Herein, we demonstrate three-dimensional highly crystalline nanostructured D(C7CO)-BTBT films via carbonyl-functionalization of a fused thienoacene π-system, and strong Raman signal enhancements in Surface-Enhanced Raman Spectroscopy (SERS) are realized. The small molecule could be prepared on the gram scale with a facile synthesis-purification. In the engineered films, polar functionalization induces favorable out-of-plane crystal growth via zigzag motif of dipolar C = O···C = O interactions and hydrogen bonds, and strengthens π-interactions. A unique two-stage film growth behavior is identified with an edge-on-to-face-on molecular orientation transition driven by hydrophobicity. The analysis of the electronic structures and the ratio of the anti-Stokes/Stokes SERS signals suggests that the π-extended/stabilized LUMOs with varied crystalline face-on orientations provide the key properties in the chemical enhancement mechanism. A molecule-specific Raman signal enhancement is also demonstrated on a high-LUMO organic platform. Our results demonstrate a promising guidance towards realizing low-cost SERS-active semiconducting materials, increasing structural versatility of organic-SERS platforms, and advancing molecule-specific sensing via molecular engineering.

Cyanido-bridged {FeIIILnIII} heterobimetallic chains assembled through the [FeIII{HB(pz)3}(CN)3]−complex as metalloligand: synthesis, crystal structure and magnetic properties

The first isostructural series of cyanido-bridged 3d–4f chains showing a unique zig-zag motif have been obtained by using the heteroleptic [FeIII{HB(pz)3}(CN)3]−complex as a metalloligand towards the preformed [LnIII(bpdo)(NO3)2(H2O)]+species.

A Vessel of the Funnel Beaker Culture at Salgótarján-Pécs-Kő

Abstract This study describes and discusses an old find from a wholly new perspective. The non-local fragment or fragments represent imports or imitations that can be linked to the Funnel Beaker culture and not to Kostolác, Coţofeni, Livezile or Bošáca as originally suggested by József Korek. The hallmarks distinctive to the culture are the ornamented rim exterior and rim interior, the zigzag motif under the rim and the ladder motif on the belly. However, the channelling on the belly is a typical Baden trait, which has not been noted on Funnel Beaker vessels to date. The best and closest analogies can be cited from the Baden settlement at Oldalfala/Stránska–Mogyorós, where they were erroneously identified as Coţofeni/Livezile imports. The occurrence of Funnel Beaker pottery on several sites on the southern fringes of the Western Carpathians suggests a more complex situation; however, their stratigraphic contexts on these multi-period, stratified sites remain unclear due to the field techniques employed during the old excavations. The determination of the exact place of origin is rather difficult within the culture’s vast distribution, although they can most likely be assigned to the Funnel Beaker eastern group, Wiórek phase (IIIB – IIIB-C in the current terminology), whose absolute dates fall between 3700/3600 and 3200 BC. The petrographic analyses revealed that the clay and the tempering agents are of local volcanic origin, providing conclusive evidence that Funnel Beaker vessels had been made locally. In this sense, the pottery fragment discussed here can be best described as a local hybrid product.

Two new 4-coordinate Cu(II) chains with 1,2,3-triazole derivate as bridging ligand: Synthesis, structures and magnetic properties

Two one-dimensional Cu(II) coordination polymers, [Cu(tdp)X2]n (X = Cl(1), Br(2), tdp = 2,2’-(1H-1,2,3-triazole-1,5-diyl)dipyridine) have been synthesized and characterized, which are the first two examples of 1D CuII chains bridging by the rigid 1,2,3-triazole ligand. Compounds 1 and 2 are isomorphous. Single-crystal X-ray diffraction revealed that the ligands bridge adjacent CuII ions into an infinite one-dimensional chain with a zigzag motif in compound 1. Meanwhile, the presence of weak face-to-face π···π interactions between pyridine ring planes of two adjacent chains leads to the stabilization of the molecular packing. DC magnetic susceptibility measurements indicated the presence of weak ferromagnetic interactions (J = 1.91 cm−1 for 1, J = 0.48 cm−1 for 2) between adjacent CuII ions within the chains and antiferromagnetic interchain coupling (J′ = −0.20 cm−1 for 1, J′ = −0.10 cm−1 for 2) due to the π···π interactions.

추상 · 과학기술 · 생명 - 한묵의 생명주의 추상

This paper aims to provide an understanding of Han Mook (1914-2016)’s abstract work of the 1970s, ones characterized by a stepped, radiating zigzag motif generated through the intersection between concentric circles and radiating lines. Titled “spirals,” “concentric circles” and “lightning rod,” his electrified geometric abstraction appeared in the early 1970s as an ambitious outcome of a prolonged status of an immigrant artist in Paris since 1961, when he left stable positions as a renowned artist, critic and educator at the age of 48 in the immediate post-Korean war years for moving to the ‘capital of the arts in the world.’ Yet the previous literature has rarely explored the historical significance of his new phase of abstract art. This paper does not rehearse the artist’s own account of his abstraction as a direct response to the 1969 Apollo 11 moon landing; nor does it consider an assumed morphological influence of the optico-kinetic forms of French and Latin American art of the time. This paper instead seeks to understand the way in which the most amazing technological feat in human history and the optico-kinetic environment of the Paris art scene of the 1960s catalyzed restoration of a particular Korean artistic discourse, a theory of vitalist or bio-centric abstraction to which Han gave a potential shape in the 1950s but which did not come into fruition at the moment. According to the discourse, art should express life, an invisible force that establishes the visible world. This paper thus allows for an understanding of Han’s use of vibrant colors, rhythmic repetitions and animated surfaces in his 1970s’ abstraction as a negotiated continuation of a largely forgotten moment of Korean vitalism.

Understanding the Origin of 2D Self-Assembly of Tricarbazole Macrocycles: An Integrated Quantum Mechanical/Molecular Dynamics Study

The intermolecular interactions underlying self-assembly are important for designing supramolecular architectures with defined function and composition over various length scales. Here, an integrated quantum mechanical/molecular dynamics (QM/MD) approach is introduced to explore the intermolecular interactions governing the two-dimensional self-assembly of a shape-persistent macrocycle, that is, tricarbazolo triazolophane (tricarb), on highly ordered pyrolytic graphite (HOPG). Three structural motifs (row, zig-zag, and rosette) for the self-association and growth of tricarb oligomers are analyzed using dispersion-corrected density functional theory to reveal their relative stability. QM analysis shows that the major factor in the self-assembly, via H-bonding contributions to the interaction energies, originates from favorable local dipole orientations between triazole units in the zig-zag and rosette motifs. Closing of the macrocyclic loop leads to the formation of a tertiary structure, which induces stab...

Synthesis of monosubstituted dipicolinic acid hydrazide derivative and structural characterization of novel Co(III) and Cr(III) complexes

A novel monosubstituted dipicolinic acid hydrazide derivative (H2L = 6-{[2-(phenylcarbonyl)hydrazino]carbonyl}pyridine-2-carboxylic acid) was prepared by the multi-step synthesis route starting from methoxy-substituted pyridine-2,6-dicarboxylic acid. Reaction of the prepared compound with Co and Cr salts in the presence of 1,6-diaminohexane resulted in formation of discrete complex compounds (CoL and CrL). The synthesized compounds were identified by chemical analyses and characterized by IR spectroscopy, thermal analysis and the ligand additionally by NMR spectroscopy. The crystal and molecular structure of the prepared complexes were determined by the single-crystal X-ray diffraction and electrochemical properties by cyclic voltammetry. The molecular structure of the complex compounds is found to be isostructural with rather small differences in the crystal packing arrangement. In both complexes the coordination geometry is octahedral and each metal ion is coordinated by two mutually orthogonal ligand molecules that act as N,N,O-tridentate ligand. In the crystal structure, the molecules are linked via multiple O–H⋯O, N–H⋯O and N–H⋯Cl hydrogen bond interactions thus forming a supramolecular zig-zag motif that is additionally stabilized by a series of hydrogen bond interactions that involve water molecule, diaminohexane cation, uncoordinated oxygen atom of carboxylic group and oxygen atom of carbonyl group. Electrochemical analysis of complex compounds indicated irreversible oxidation of Cr3+ in CrL and reduction of Co3+ to Co2+ in CoL, which agrees with the proposed oxidation state of the metal in complexes.

Pántkarperecek a magyar honfoglalás korából

The author collected the material of ca. 250 find places by types. He examined the material, manufacturing technique, and chronology of the bracelets, as well as their distribution by social layers and gender, and their direct analogies in Russia and the Balkans. The ancient Hungarians of the Conquest period appeared in the Carpathian Basin with a new archaeological culture in the turn of the 9th and the 10th centuries. Band bracelets were characteristic pieces of this material culture. Today they are represented by three main types: 1. band with rounded terminals, 2. band with coiled terminals, 3. hinged band. The first type has many variants. The terminal of the bracelet can be disc-like rounded, but mostly it just ends in a semicircular form. The band can be undecorated, decorated with punched palmette-tendril ornaments, or sometimes with geometric (zigzag) motifs, and applied decoration can also appear at the end of the band. In the beginning of the 11th century only bronze bands occurred, with various punched dotted circle decorations. A punched hole can often be observed at both ends of the bands. This might have served for sewing the band on, however, others believe that a string threaded through the holes pulled the band together. The most frequent decorations of bracelets with coiled terminals are punched zigzag motifs, and sometimes palmette-tendrils also occurs. While the former type is frequent by both men and women, bracelets with twisted terminals rarely occur by men. Hinged bracelets either copied Byzantine antecedents, or they arrived as imports. The ends of the sleeves of the funerary dress, the cuffs were decorated by thin silver or gold ribbons that were sewed on the hem of the dress.

Triphenylbismuth(v) di[(iso)nicotinates] - transmetallation agents or divergent organometalloligands? First organobismuth(v)-based silver(i) coordination polymers.

The reaction of Ph3BiCl2 with alkali salts of isonicotinic and nicotinic acids afforded Ph3Bi[O(O)CC5H4N-4]2 (1) and Ph3Bi[O(O)CC5H4N-3]2 (2), respectively, which were characterized by multinuclear NMR spectroscopy in solution, mass spectrometry and IR spectroscopy in the solid state. Their molecular structures were established by single-crystal X-ray diffraction. For both 1 and 2 the molecules contain a trigonal bipyramidal C3BiO2 core, with the phenyl groups in equatorial positions. The potential use of 1 and 2 as ditopic organometalloligands was investigated. The reaction of 1 or 2 with Me3SnCl (1 : 2 molar ratio) resulted in carboxylato ligand exchange and the formation of Me3Sn[O(O)CC5H4N-4] (3) and Me3Sn[O(O)CC5H4N-3] (4) besides Ph3BiCl2. The crystals of both 3 and 4 contain 1-D coordination polymers built through intermolecular N → Sn interactions. The treatment of Ni[S2P(OiPr)2]2 with 1 and 2, respectively, resulted, in addition to di(carboxylato)nickel(ii) derivatives, in isolation of Ph3Bi and the disulphane [(iPrO)2P(S)S]2. New coordination polymers were obtained by reacting 1 and 2 with various silver(i) salts: [Ag{Ph3Bi[O(O)CC5H4N-4]2}(OTf)] (5), [Ag{Ph3Bi[O(O)CC5H4N-3]2}(OTf)]·CH2Cl2 (6·CH2Cl2), [Ag{Ph3Bi[O(O)CC5H4N-4]2}](SbF6)·2THF (7·2THF), [Ag{Ph3Bi[O(O)CC5H4N-3]2}](SbF6)·CH2Cl2 (8·CH2Cl2) and [Ag{Ph3Bi[O(O)CC5H4N-3]2}(NO3)]·CH2Cl2 (9·CH2Cl2). The crystal structures of 5 and 6 can be described as 1-D chains linked by triflate bridges in pairs of chains and 2-D networks, respectively. Compound 7 features a 2-D grid-like topology of the network, with tecton 1 acting as a tridentate ligand through both nitrogen and one oxygen atoms. The linker 2 molecules adopt either cis (compound 6) or trans (compounds 8 and 9) conformation. Complexes 8 and 9 are 1-D chain polymers exhibiting zig-zag and wavy motifs, respectively. The dimensionality of the structures is extended by the presence of supramolecular interactions (ππ, AgAg, AgO).

Recognition of C60 by tetra- and tri-quinoxaline cavitands

Molecular recognition of C60 fullerene by two cavitands, bearing four and three quinoxaline walls, is reported here. Fluorescence titrations show the recognition ability of the receptors with high binding constant values. The formation of a stable 1:1 supramolecular complex was also confirmed by DOSY, EI-MS and X-ray analysis. The crystal structure analysis of tetraquinoxaline cavitand and C60 shows a crystal packing, where C60 molecules are intercalated between bilayers of cavitand molecules, on the ideal fourfold symmetry axis of the receptor, and are arranged in a zigzag motif.

Metal-dependent ribbon and self-penetrated topologies in nitroaromatic-sensing zinc and cadmium coordination polymers with terephthalate and dipyridylamide ligands

Hydrothermal reaction of the requisite metal nitrate, potassium terephthalate (K2tere) and the dipyridylamide 3-pyridylisonicotinamide (3-pina) afforded a pair of crystalline coordination polymers whose dimensionality and topology depends critically on the metal coordination environment. The two new crystalline phases were structurally characterized via single-crystal X-ray diffraction. {[Zn(tere)(3-pina)2]·2H2O}n (1) manifests a 1-D zig-zag ribbon motif with monodentate 3-pina ligands. [Cd(tere)(3-pina)2]n (2) displays a self-penetrated 3-D network with 446108 mab topology. Thermal and luminescent properties of these two new materials are also presented. Both 1 and 2 show capability as sensors for nitroaromatic compounds via luminescence quenching, with better absorption for nitrobenzene than the more sterically bulky analyte m-nitrophenol.

Across the River. The Cemetery in Dolina and New Aspects of the Late Urnfield Culture in Croatian Posavina and Northern Bosnia

The site of Dolina in the Croatian region of Posavina has been investigated since 2009 under the leadership of the Institute of Archaeology in Zagreb. In previous excavations five tumuli with one or two cremation deposits of different types (urned, scattered cremation remains, or with an organic container) could be detected. On the basis of characteristic grave goods (bronze pins and fibulae, helmet parts), the burials are dated to the 9th-8th century BC or in the stage Ha B3-Ha C1. Typical of Dolina, but also of other sites in Croatia and Bosnia along the middle course of the Sava River (e.g. Donja Dolina), is the ensemble of finds (jewellery, weapons and ceramics) of different regional origin, which underlines the specific position of this region at the interface between the Carpathian Basin to the north, the Alps to the west, the Balkans to the south and the lower Danube to the east. Vessels with incised zigzag motifs from Tumuli 6 and 8 reveal communication with the neighbouring area of northern Bosnia. Similar ornamentation appears there in contemporaneous settlement layers (at Vis and Zecovi) and in the corresponding cremation burials in flat graves (Petkovo Brdo and Mekota). However, the establishment of tumuli at Dolina, and various burial rites with different grave goods, emphasise a strong local component and a distinct individualisation of the graves, i.e. as buried members of a particular but heterogeneous community.

A new class of ion-ion interaction: Z-bond

The hydrogen-bond interactions in ionic liquids have been simply described by the conventional hydrogen-bond model of A-H…B. Coupling with the strong electrostatic force, however, hydrogen bond between the cation and anion shows particular features in the geometric, energetic, electronic, and dynamic aspects, which is inherently different from that of the conventional hydrogen bond. A general model could be expressed as +[A-H…B]-, in which A and B represent heavy atoms and + and - represent the charges of the cation containing A atom and anion containing B atom, respectively. Because the structure shows a zig-zag motif, this coupling interaction is defined here as the Z-bond. The new model could be generally used to describe the interactions in ionic liquids, as well as bio-systems involved in ions, ionic reaction, and ionic materials.

Cyano-bridged heterometallic complexes directed by binuclear copper units

A tridentate N,O-donor, 1,3-bis(3,5-dimethylpyrazol-1-yl)propan-2-ol (HL), has been employed to synthesize cyano-bridged complexes and six heterometallic complexes with [Cu2L2] or [Cu2L2(H2O)] have been generated by using slow diffusion. With slightly different synthetic conditions, subtle variations in the crystal structures of the complexes occur. [Cu2L2][Fe(CN)5NO]⋅2CH3CN (1) and [Cu2L2][Fe(CN)5NO]⋅H2O (2), synthesized in different solvents with the same precursor, exhibit a very similar 1-D zig-zag chain motif in different space groups, P21 and P-1, respectively. Similarly, [Cu2L2(H2O)][Ni(CN)4]·H2O (3) and [Cu2L2][Ni(CN)4]⋅H2O (4), synthesized with different diffusion methods, feature trinuclear and 1-D zig-zag chain structures, which indicates a solvent effect of water. [Cu2L2(H2O)]2[Cu2L2][W(CN)8]2·8H2O (5) is composed of two [W(CN)8]3− and three [Cu2L2]2+ units. In the octanuclear structure, [W(CN)8]3− and one [Cu2L2]2+ bridge and the other two [Cu2L2]2+ are terminal to stop extending the 1-D structure. [CuL][Ag2.24Cu0.76(CN)4] (6) exhibits a discrete structure, in which the complex anion forms a unique 2-D 63 network and the complex cations are inserted in the space between two adjacent networks. Magnetic properties of 1 and 4 are discussed.

A Bimetallic Chain Based on [Mo(CN)8]3− and Ho3+ Ions as Building Blocks

A novel bimetallic 4d-4f complex, {[HoIII(DMF)6] [MoV(CN)8]·3H2O}n (1) (DMF = N,N’-dimethylformamide), has been synthesized and structurally characterized. The crystalline analyses shown that the complex 1 consists of a one-dimensional (1D) infinite chain, which adopts a 1D zigzag motif, and this is the first structurally characterized example of a 1D structure based on the [Mo(CN)8]3− and Ho3+ building blocks. The complex 1 crystallizes in a monoclinic system of space group P21/c, with a = 10.8672(7), b = 20.920(2), c = 17.9097(7) Å, β = 92.646(4)°, and Z = 4.

Ethyl 2-[(carbamoylamino)imino]propanoate hemihydrate

The title compound, C6H11N3O3·0.5H2O, has two independent mol­ecules and one mol­ecule of water in the asymmetric unit. The crystal packing is stabilized by inter­molecular N—H⋯N, O—H⋯O, N—H⋯O and C—H⋯O hydrogen bonds. These inter­actions form a two-dimensional array in the ab plane with a zigzag motif which has an angle close to 35° between the zigzag planes. The hydrogen bonding can be best described using the graph-set notation as N 1 = C(10)R 2 2(10)R 2 2(8) and N 2 = R 6 4(20)R 2 2(8).