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Computational Design Framework 3D Graphic Statics
Computational Design Framework for 3D Graphic Statics 3D Graphic for Computational Design Framework Computational Design Framework for 3D Graphic Statics Juney Lee Juney Lee Juney ETH Zurich • PhD Dissertation No. 25526 Diss. ETH No. 25526 DOI: 10.3929/ethz-b-000331210 Computational Design Framework for 3D Graphic Statics A thesis submitted to attain the degree of Doctor of Sciences of ETH Zurich (Dr. sc. ETH Zurich) presented by Juney Lee 2015 ITA Architecture & Technology Fellow Supervisor Prof. Dr. Philippe Block Technical supervisor Dr. Tom Van Mele Co-advisors Hon. D.Sc. William F. Baker Prof. Allan McRobie PhD defended on October 10th, 2018 Degree confirmed at the Department Conference on December 5th, 2018 Printed in June, 2019 For my parents who made me, for Dahmi who raised me, and for Seung-Jin who completed me. Acknowledgements I am forever indebted to the Block Research Group, which is truly greater than the sum of its diverse and talented individuals. The camaraderie, respect and support that every member of the group has for one another were paramount to the completion of this dissertation. I sincerely thank the current and former members of the group who accompanied me through this journey from close and afar. I will cherish the friendships I have made within the group for the rest of my life. I am tremendously thankful to the two leaders of the Block Research Group, Prof. Dr. Philippe Block and Dr. Tom Van Mele. This dissertation would not have been possible without my advisor Prof. Block and his relentless enthusiasm, creative vision and inspiring mentorship. -
Magneto-Luminescence Correlation in the Textbook Dysprosium(III
Magnetochemistry 2016, 2, 41; doi:10.3390/magnetochemistry2040041 S1 of S3 Supplementary Materials: Magneto‐Luminescence Correlation in the Textbook Dysprosium(III) Nitrate Single‐Ion Magnet Ekaterina Mamontova, Jérôme Long, Rute A. S. Ferreira, Alexandre M. P. Botas, Dominique Luneau, Yannick Guari, Luis D. Carlos and Joulia Larionova Table S1. Crystal and structure refinement data for compound 1. Compound 1 Formula DyH12N3O15 Formula weight 456.60 Temperature/K 293 Crystal system Triclinic Space group P‐1 a/Å 6.7429(8) b/Å 9.1094(9) c/Å 11.6502(11) α/° 70.369(9) β/° 88.714(9) γ/° 69.113(11) Volume/Å3 625.86(13) Z 2 Dc/g∙cm−3 2.4228 μ(Mo‐Kα)/mm−1 6.054 F(000) 414.2 Crystal size/mm 0.1 × 0.1 × 0.1 Crystal type Colourless plates range 3.25 to 29.29 −9 ≤ h ≤ 9 Index ranges −12 ≤ k ≤ 11 −14 ≤ l ≤ 14 Reflections collected 5351 Independent reflections 2879 (Rint = 0.0424) Data/parameters 2879/171 R1 = 0.0369 Final R indices [I > 2σ(I)]a,b wR2 = 0.0765 R1 = 0.0443 Final R indices (all data)a,b wR2 = 0.0848 Largest diff. peak and hole 1.18 and −1.64 eÅ−3 a b 2222 2 RFFF1 / ; wR2 w F F/ w F oc o oc o Magnetochemistry 2016, 2, 41 S2 of S3 Table S2. SHAPE analysis for compound 1. DP EPY OBPY PPR PAPR JBCCU JPCSAPR JMBIC JATDI JSPC SDD TD HD 33.818 23.117 17.902 9.556 14.372 11.933 4.385 8.791 17.518 2.204 6.675 6.077 10.278 DP, decagon; EPY, ennegonal pyramid; OBPY, octagonal pyramid; PPR, pentagonal prism; PAPR, pentagonal antiprism; JBCCU, bicapped cube; JPCSPAR, bicapped square antiprism; JMBIC, metabidiminished icosahedron; JATDI, augmented tridiminished icosahedron; JSPC, spherocorona; SDD, staggered dodecahedron; TD, tetradecahedron; HD, hexadecahedron. -
Article Published Under an ACS Authorchoice License, Which Permits Copying and Redistribution of the Article Or Any Adaptations for Non-Commercial Purposes
This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes. Article www.acsnano.org Standardizing Size- and Shape-Controlled Synthesis of Monodisperse Magnetite (Fe3O4) Nanocrystals by Identifying and Exploiting Effects of Organic Impurities † † † ‡ † † † § Liang Qiao, Zheng Fu, Ji Li, , John Ghosen, Ming Zeng, John Stebbins, Paras N. Prasad, † and Mark T. Swihart*, † § Department of Chemical and Biological Engineering and Institute for Lasers, Photonics, Biophotonics, University at Buffalo (SUNY), Buffalo, New York 14260, United States ‡ MIIT Key Laboratory of Critical Materials Technology for New Energy Conversion and Storage, School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China *S Supporting Information ABSTRACT: Magnetite (Fe3O4) nanocrystals (MNCs) are among the most-studied magnetic nanomaterials, and many reports of solution-phase synthesis of monodisperse MNCs have been published. However, lack of reproducibility of MNC synthesis is a persistent problem, and the keys to producing monodisperse MNCs remain elusive. Here, we define and explore synthesis parameters in this system thoroughly to reveal their effects on the product MNCs. We demonstrate the essential role of benzaldehyde and benzyl benzoate produced by oxidation of benzyl ether, the solvent typically used for MNC synthesis, in producing mono- disperse MNCs. This insight allowed us to develop stable formulas for producing monodisperse MNCs and propose a model to rationalize MNC size and shape evolution. Solvent polarity controls the MNC size, while short ligands shift the morphology from octahedral to cubic. We demonstrate preparation of specific assemblies with these MNCs. -
The Mars Pentad Time Pyramids the Quantum Space Time Fractal Harmonic Codex the Pentagonal Pyramid
The Mars Pentad Time Pyramids The Quantum Space Time Fractal Harmonic Codex The Pentagonal Pyramid Abstract: Early in this author’s labors while attempting to create the original Mars Pentad Time Pyramids document and pyramid drawings, a failure was experienced trying to develop a pentagonal pyramid with some form of tetrahedral geometry. This pentagonal pyramid is now approached again and refined to this tetrahedral criteria, creating tetrahedral angles in the pentagonal pyramid, and pentagonal [54] degree angles in the pentagon base for the pyramid. In the process another fine pentagonal pyramid was developed with pure pentagonal geometries using the value for ancient Egyptian Pyramid Pi = [22 / 7] = [aPi]. Also used is standard modern Pi and modern Phi in one of the two pyramids shown. Introduction: Achieved are two Pentagonal Pyramids: One creates tetrahedral angle [54 .735~] in the Side Angle {not the Side Face Angle}, using a novel height of the value of tetrahedral angle [19 .47122061] / by [5], and then the reverse tetrahedral angle is accomplished with the same tetrahedral [19 .47122061] angle value as the height, but “Harmonic Codexed” to [1 .947122061]! This achievement of using the second height mentioned, proves aspects of the Quantum Space Time Fractal Harmonic Codex. Also used is Height = [2], which replicates the [36] and [54] degree angles in the pentagon base to the Side Angles of the Pentagonal Pyramid. I have come to understand that there is not a “perfect” pentagonal pyramid. No matter what mathematical constants or geometry values used, there will be a slight factor of error inherent in the designs trying to attain tetrahedra. -
Pentagonal Pyramid
Chapter 9 Surfaces and Solids Copyright © Cengage Learning. All rights reserved. Pyramids, Area, and 9.2 Volume Copyright © Cengage Learning. All rights reserved. Pyramids, Area, and Volume The solids (space figures) shown in Figure 9.14 below are pyramids. In Figure 9.14(a), point A is noncoplanar with square base BCDE. In Figure 9.14(b), F is noncoplanar with its base, GHJ. (a) (b) Figure 9.14 3 Pyramids, Area, and Volume In each space pyramid, the noncoplanar point is joined to each vertex as well as each point of the base. A solid pyramid results when the noncoplanar point is joined both to points on the polygon as well as to points in its interior. Point A is known as the vertex or apex of the square pyramid; likewise, point F is the vertex or apex of the triangular pyramid. The pyramid of Figure 9.14(b) has four triangular faces; for this reason, it is called a tetrahedron. 4 Pyramids, Area, and Volume The pyramid in Figure 9.15 is a pentagonal pyramid. It has vertex K, pentagon LMNPQ for its base, and lateral edges and Although K is called the vertex of the pyramid, there are actually six vertices: K, L, M, N, P, and Q. Figure 9.15 The sides of the base and are base edges. 5 Pyramids, Area, and Volume All lateral faces of a pyramid are triangles; KLM is one of the five lateral faces of the pentagonal pyramid. Including base LMNPQ, this pyramid has a total of six faces. The altitude of the pyramid, of length h, is the line segment from the vertex K perpendicular to the plane of the base. -
Putting the Icosahedron Into the Octahedron
Forum Geometricorum Volume 17 (2017) 63–71. FORUM GEOM ISSN 1534-1178 Putting the Icosahedron into the Octahedron Paris Pamfilos Abstract. We compute the dimensions of a regular tetragonal pyramid, which allows a cut by a plane along a regular pentagon. In addition, we relate this construction to a simple construction of the icosahedron and make a conjecture on the impossibility to generalize such sections of regular pyramids. 1. Pentagonal sections The present discussion could be entitled Organizing calculations with Menelaos, and originates from a problem from the book of Sharygin [2, p. 147], in which it is required to construct a pentagonal section of a regular pyramid with quadrangular F J I D T L C K H E M a x A G B U V Figure 1. Pentagonal section of quadrangular pyramid basis. The basis of the pyramid is a square of side-length a and the pyramid is assumed to be regular, i.e. its apex F is located on the orthogonal at the center E of the square at a distance h = |EF| from it (See Figure 1). The exercise asks for the determination of the height h if we know that there is a section GHIJK of the pyramid by a plane which is a regular pentagon. The section is tacitly assumed to be symmetric with respect to the diagonal symmetry plane AF C of the pyramid and defined by a plane through the three points K, G, I. The first two, K and G, lying symmetric with respect to the diagonal AC of the square. -
2D and 3D Shapes.Pdf
& • Anchor 2 - D Charts • Flash Cards 3 - D • Shape Books • Practice Pages rd Shapesfor 3 Grade by Carrie Lutz T hank you for purchasing!!! Check out my store: http://www.teacherspayteachers.com/Store/Carrie-Lutz-6 Follow me for notifications of freebies, sales and new arrivals! Visit my BLOG for more Free Stuff! Read My Blog Post about Teaching 3 Dimensional Figures Correctly Credits: Carrie Lutz©2016 2D Shape Bank 3D Shape Bank 3 Sided 5 Sided Prisms triangular prism cube rectangular prism triangle pentagon 4 Sided rectangle square pentagonal prism hexagonal prism octagonal prism Pyramids rhombus trapezoid 6 Sided 8 Sided rectangular square triangular pyramid pyramid pyramid Carrie LutzCarrie CarrieLutz pentagonal hexagonal © hexagon octagon © 2016 pyramid pyramid 2016 Curved Shapes CURVED SOLIDS oval circle sphere cone cylinder Carrie Lutz©2016 Carrie Lutz©2016 Name _____________________ Side Sort Date _____________________ Cut out the shapes below and glue them in the correct column. More than 4 Less than 4 Exactly 4 Carrie Lutz©2016 Name _____________________ Name the Shapes Date _____________________ 1. Name the Shape. 2. Name the Shape. 3. Name the Shape. ____________________________________ ____________________________________ ____________________________________ 4. Name the Shape. 5. Name the Shape. 6. Name the Shape. ____________________________________ ____________________________________ ____________________________________ 4. Name the Shape. 5. Name the Shape. 6. Name the Shape. ____________________________________ ____________________________________ ____________________________________ octagon circle square rhombus triangle hexagon pentagon rectangle trapezoid Carrie Lutz©2016 Faces, Edges, Vertices Name _____________________ and Date _____________________ 1. Name the Shape. 2. Name the Shape. 3. Name the Shape. ____________________________________ ____________________________________ ____________________________________ _____ faces _____ faces _____ faces _____Edges _____Edges _____Edges _____Vertices _____Vertices _____Vertices 4. -
Hexagonal Antiprism Tetragonal Bipyramid Dodecahedron
Call List hexagonal antiprism tetragonal bipyramid dodecahedron hemisphere icosahedron cube triangular bipyramid sphere octahedron cone triangular prism pentagonal bipyramid torus cylinder squarebased pyramid octagonal prism cuboid hexagonal prism pentagonal prism tetrahedron cube octahedron square antiprism ellipsoid pentagonal antiprism spheroid Created using www.BingoCardPrinter.com B I N G O hexagonal triangular squarebased tetrahedron antiprism cube prism pyramid tetragonal triangular pentagonal octagonal cube bipyramid bipyramid bipyramid prism octahedron Free square dodecahedron sphere Space cuboid antiprism hexagonal hemisphere octahedron torus prism ellipsoid pentagonal pentagonal icosahedron cone cylinder prism antiprism Created using www.BingoCardPrinter.com B I N G O triangular pentagonal triangular hemisphere cube prism antiprism bipyramid pentagonal hexagonal tetragonal torus bipyramid prism bipyramid cone square Free hexagonal octagonal tetrahedron antiprism Space antiprism prism squarebased dodecahedron ellipsoid cylinder octahedron pyramid pentagonal icosahedron sphere prism cuboid spheroid Created using www.BingoCardPrinter.com B I N G O cube hexagonal triangular icosahedron octahedron prism torus prism octagonal square dodecahedron hemisphere spheroid prism antiprism Free pentagonal octahedron squarebased pyramid Space cube antiprism hexagonal pentagonal triangular cone antiprism cuboid bipyramid bipyramid tetragonal cylinder tetrahedron ellipsoid bipyramid sphere Created using www.BingoCardPrinter.com B I N G O -
Novel Magnetic Materials Based on Macrocyclic Ligands: Towards High Relaxivity Contrast Agents and Mononuclear Single-Molecule Magnets
Novel Magnetic Materials Based on Macrocyclic Ligands: Towards High Relaxivity Contrast Agents and Mononuclear Single-Molecule Magnets Emma Stares A thesis submitted to the Department of Chemistry in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Supervised by Professor Melanie Pilkington Brock University St. Catharines Ontario, Canada August 2015 © Emma Stares, 2015 Abstract The preparation and characterization of coordination complexes of Schiff-base and crown ether macrocycles is presented, for application as contrast agents for magnetic resonance imaging, Project 1; and single-molecule magnets (SMMs), Projects 2 and 3. II III In Project 1, a family of eight Mn and Gd complexes of N3X2 (X = NH, O) and N3O3 Schiff-base macrocycles were synthesized, characterized, and evaluated as potential contrast agents for MRI. In vitro and in vivo (rodent) studies indicate that the studied complexes display efficient contrast behaviour, negligible toxicity, and rapid excretion. III In Project 2, Dy complexes of Schiff-base macrocycles were prepared with a view to developing a new family of mononuclear Ln-SMMs with pseudo-D5h geometries. Each complex displayed slow relaxation of magnetization, with magnetically-derived energy barriers in the range Ueff = 4 – 24 K. In Project 3, coordination complexes of selected later lanthanides with various crown ether ligands were synthesized. Two families of complexes were structurally and magnetically analyzed: ‘axial’ or sandwich-type complexes based on 12-crown-4 and 15- crown-5; and ‘equatorial’ complexes based on 18-crown-6. Magnetic data are supported by ab initio calculations and luminescence measurements. Significantly, the first mononuclear Ln-SMM prepared from a crown ether ligand is described. -
[ENTRY POLYHEDRA] Authors: Oliver Knill: December 2000 Source: Translated Into This Format from Data Given In
ENTRY POLYHEDRA [ENTRY POLYHEDRA] Authors: Oliver Knill: December 2000 Source: Translated into this format from data given in http://netlib.bell-labs.com/netlib tetrahedron The [tetrahedron] is a polyhedron with 4 vertices and 4 faces. The dual polyhedron is called tetrahedron. cube The [cube] is a polyhedron with 8 vertices and 6 faces. The dual polyhedron is called octahedron. hexahedron The [hexahedron] is a polyhedron with 8 vertices and 6 faces. The dual polyhedron is called octahedron. octahedron The [octahedron] is a polyhedron with 6 vertices and 8 faces. The dual polyhedron is called cube. dodecahedron The [dodecahedron] is a polyhedron with 20 vertices and 12 faces. The dual polyhedron is called icosahedron. icosahedron The [icosahedron] is a polyhedron with 12 vertices and 20 faces. The dual polyhedron is called dodecahedron. small stellated dodecahedron The [small stellated dodecahedron] is a polyhedron with 12 vertices and 12 faces. The dual polyhedron is called great dodecahedron. great dodecahedron The [great dodecahedron] is a polyhedron with 12 vertices and 12 faces. The dual polyhedron is called small stellated dodecahedron. great stellated dodecahedron The [great stellated dodecahedron] is a polyhedron with 20 vertices and 12 faces. The dual polyhedron is called great icosahedron. great icosahedron The [great icosahedron] is a polyhedron with 12 vertices and 20 faces. The dual polyhedron is called great stellated dodecahedron. truncated tetrahedron The [truncated tetrahedron] is a polyhedron with 12 vertices and 8 faces. The dual polyhedron is called triakis tetrahedron. cuboctahedron The [cuboctahedron] is a polyhedron with 12 vertices and 14 faces. The dual polyhedron is called rhombic dodecahedron. -
Computer-Aided Design Disjointed Force Polyhedra
Computer-Aided Design 99 (2018) 11–28 Contents lists available at ScienceDirect Computer-Aided Design journal homepage: www.elsevier.com/locate/cad Disjointed force polyhedraI Juney Lee *, Tom Van Mele, Philippe Block ETH Zurich, Institute of Technology in Architecture, Block Research Group, Stefano-Franscini-Platz 1, HIB E 45, CH-8093 Zurich, Switzerland article info a b s t r a c t Article history: This paper presents a new computational framework for 3D graphic statics based on the concept of Received 3 November 2017 disjointed force polyhedra. At the core of this framework are the Extended Gaussian Image and area- Accepted 10 February 2018 pursuit algorithms, which allow more precise control of the face areas of force polyhedra, and conse- quently of the magnitudes and distributions of the forces within the structure. The explicit control of the Keywords: polyhedral face areas enables designers to implement more quantitative, force-driven constraints and it Three-dimensional graphic statics expands the range of 3D graphic statics applications beyond just shape explorations. The significance and Polyhedral reciprocal diagrams Extended Gaussian image potential of this new computational approach to 3D graphic statics is demonstrated through numerous Polyhedral reconstruction examples, which illustrate how the disjointed force polyhedra enable force-driven design explorations of Spatial equilibrium new structural typologies that were simply not realisable with previous implementations of 3D graphic Constrained form finding statics. ' 2018 Elsevier Ltd. All rights reserved. 1. Introduction such as constant-force trusses [6]. However, in 3D graphic statics using polyhedral reciprocal diagrams, the influence of changing Recent extensions of graphic statics to three dimensions have the geometry of the force polyhedra on the force magnitudes is shown how the static equilibrium of spatial systems of forces not as direct or intuitive. -
Crystal Chemical Relations in the Shchurovskyite Family: Synthesis and Crystal Structures of K2cu[Cu3o]2(PO4)4 and K2.35Cu0.825[Cu3o]2(PO4)4
crystals Article Crystal Chemical Relations in the Shchurovskyite Family: Synthesis and Crystal Structures of K2Cu[Cu3O]2(PO4)4 and K2.35Cu0.825[Cu3O]2(PO4)4 Ilya V. Kornyakov 1,2 and Sergey V. Krivovichev 1,3,* 1 Department of Crystallography, Institute of Earth Sciences, St. Petersburg State University, University Emb. 7/9, 199034 Saint-Petersburg, Russia; [email protected] 2 Laboratory of Nature-Inspired Technologies and Environmental Safety of the Arctic, Kola Science Centre, Russian Academy of Science, Fesmana 14, 184209 Apatity, Russia 3 Nanomaterials Research Center, Federal Research Center–Kola Science Center, Russian Academy of Sciences, Fersmana Str. 14, 184209 Apatity, Russia * Correspondence: [email protected] Abstract: Single crystals of two novel shchurovskyite-related compounds, K2Cu[Cu3O]2(PO4)4 (1) and K2.35Cu0.825[Cu3O]2(PO4)4 (2), were synthesized by crystallization from gaseous phase and structurally characterized using single-crystal X-ray diffraction analysis. The crystal structures of both compounds are based upon similar Cu-based layers, formed by rods of the [O2Cu6] dimers of oxocentered (OCu4) tetrahedra. The topologies of the layers show both similarities and differences from the shchurovskyite-type layers. The layers are connected in different fashions via additional Cu atoms located in the interlayer, in contrast to shchurovskyite, where the layers are linked by Ca2+ cations. The structures of the shchurovskyite family are characterized using information-based Citation: Kornyakov, I.V.; structural complexity measures, which demonstrate that the crystal structure of 1 is the simplest one, Krivovichev, S.V. Crystal Chemical whereas that of 2 is the most complex in the family.