Cambridge University Press 978-1-107-41160-9 - New Geometries for New Materials Eric a Lord, Alan L Mackay and S Ranganathan Index More Information

Cambridge University Press 978-1-107-41160-9 - New Geometries for New Materials Eric A Lord, Alan L Mackay and S Ranganathan Index More information

Index

Page numbers in italics refer to illustrations

-Al–Mn–Si, 57 Aston, M. W., 67 -boron, 89 asymmetric unit, 11, 50, 172 -helix, 207 Atiyah, M. & Sutcliffe, P., 109 -manganese, 100, 101, 153, 192, 203 Atlas of Zeolite Framework Types, 126, 136, Abe, E. et al., 200 139 AcrobatReader, 210 Audier, M. et al., 94, 202 Acta Crystallographica, 133, 203 Audier, M. & Duneau, M., 76 adjoint surfaces, 163 Audier, M. & Guyot, P., 85, 86, 102, 106 Al–Co, 104 Algorithmic Beauty of Plants, The,78 -brass 194 alloys, 193 -crystobalite, 41, 137, 139 Almagest, 4 -manganese, 114, 115, 207 Almgren, F. J., 162 -quartz, 111, 138, 139, 144 Al–Mn, 102, 105 -tungsten (-W), 44, 45, 145 Al–Ni–Co, 21, 104, 105, 201 Baer, S., 107 aluminosilicate, 136 Baerlocher, Ch. et al., 136, 137, 139 Amelinckx et al., 121 balance surface, 14, 149, 168 Ammann, R., 18, 55, 199 Barlow, W., 4 Ammann bars, 16 BASIC, 209 Ammann tilings, 85, 86 Baumé, A., 3 Anaxagoras, 1 Bausch, A. R. et al., 71 Andersson, S., 161 Belin, C. H. E. & Belin, R. C. H., 98 Andersson, S. & Hyde, S. T., 182, 186 Bergman, G. et al., 92, 94, 202 Andreini, A., 36 Bergman cluster, 91, 92, 95, 203 anti-Kythera mechanism, 1 Bernard, C., 6 aperiodic tiling, 16, 55, 84, 85 Bernal, J. D., 66, 198, 199, 204 Applebaum, J. & Weiss, Y., 69 Bernal, J. D. & Carlisle, C. H., 6 approximants, 56 Bernal deltahedra, 66, 205 Archimedes, 1 Bilinski, S., 57 Archimedean screw, 180, 181 Birmingham Cluster Database, 109 Archimedean solids, 2, 24, 133 Blatov, V. A. & Shevchenko, A. P., 42 Aryabhata, 190 Blum, Z. et al., 182 Aryabhatiya, 190 Boerdijk, A. H., 64, 207 Ashmolean Museum, Oxford, 3 Boerdijk-Coxeter helix, 64, 107, 112, 207 Astbury, W., 198 Bolyai, J., 3 Aste, T., 73 Bonnet transformation, 163, 169, 173 Aste, T. & Weaire, D., 61 Booth, D., 107

231

© in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-41160-9 - New Geometries for New Materials Eric A Lord, Alan L Mackay and S Ranganathan Index More information

232 Index

boracil, 152 conical helix, 110 boron, 41, 89 connectivity, 13, 27 Boström, M. & Lidin, S., 115, 116, 207 Consortium of Theoretical Frameworks, 144 Bourgoin, J., 10 constant mean curvature, Bradley, A. J. & Jones, P., 95, 97, 195 Conway, J. H., 12 Bradley, A. J. & Thewlis, J., 97, 195 Conway J. H. & Huson, D. H., 12 Bragg, W. H. & Bragg, W. L., 4 Conway, J. H. & Knowles, K. M., 18 Brakke, K., x, 52, 162, 172, 210 Conway, J. H. & Sloane, N. J. A., 67, 68, 72 branched catenoid, 169, 170 Cook, T. A., 110, 121 branch point, 172, 178 coordination, 75 Bravais, A. & Bravais, L., 122 coordination number (CN), 191, 193, 202 Bravais lattices, 32, 33, 191 coordination polyhedron, 41 Brunner, G. O., 153 coordination sequence, 135, 140, 146 buckling pattern, 127, 128 CorelDraw, 210 Buckminster Fuller, R., ix, 64, 72 Cornelli, A. et al., 42. Bucky ball, ix, 93 Costa, C., 164 bulk metallic glasses (BMG), 204 Costa’s surface, 164 Burgers vector 13, 14 Cottrell, A. H., 191, 194 counterchange pattern, 14 -brass, 195, 196, 202 Coxeter, H. S. M., 6, 7, 12, 15, 43, 47, 64, 119, 122, -brass clusters, 65, 194 125, 132, 162, 175 -phases, 194 Coxeter, H. S. M. & Moser, W. O. J., 12 -unit, 156 Coxeter group, 51 cactus, 127 Coxeter helix, 64 Caltech, 204 Coxeter-Petrie polygons, 153 Cambridge Cluster Database, 109 Coxeter-Petrie polyhedra, 132, 149, 152, 175 carbon nanotubes, 119 C(P), 135, 167, 184 catenoid, 162, 163 crankshaft, 141 CaTiO3 (perovskite), 41 Critchlow, K., 3, 36 ccp, 191 Critchlow, K. & Nasr, S. H., 10 C(D), 171, 184 Cromwell, P. R., 24 Cd3Cu4, 89 Crowe, D. W., 14 cellular structures, 36 crystallography, 4 Chabot, B. et al., 95, 161, 203 crystalloids, 107 Chalifour, G., 3 crystal system, 34 Chattopadhyay, K. et al., 197, 200 cubic close packing, 6, 61, 191 Chen, B. et al., 160 cubic hexagonal lattice, 203 chlorine hydrate, 48, 137, 141, 208 cuboctahedron, 191 C(H), 170 Cundy, H. M. & Rollet, A. P., 24, 67 Chorbachi, W. K., 10 curvature Chung F. & Sternberg, S., 29 Gaussian, 4, 28, 120, 162, 172, 188 Church, A. H., 122 mean, 162, 186, 188 circle packing, 59 principal curvatures, 28, 162 Clare, B. W. & Kepert, D. L., 68 Curves of Life, The, 110 clathrates, 49, 137, 208 cylindrical hexagonal lattice (CHL), 128, 129 Clifford translation, 119 close packing, 75, 190 -Co2Zn15, 116 CLP, 167 daisy, 123 clusters, 88 Davis, M. E., 161 of icosahedra, 88, 91 de Bruijn, N. G., 18, 199 of icosahedra and octahedra, 101 Debye-Scherrer X-ray pattern, 192 of tetrahedra and octahedra, 101 decagonal quasicrystal, 21 triacontahedral, 106 De Divina Proportione, 22 cluster-packing model, 206 Delaney symbol, 146 collagen, 65, 207 Delgado-Friedrichs, O. & Huson, D. H., 12, 44, 51, Cockayne, E. & Widom, M., 104 149 collagen, 119 Delgado-Friedrichs, O. & O’Keeffe, M., 148 coloured symmetry, 14 Delgado-Friedrichs et al., 134, 146, 148 Coloured Symmetry, 15 Delone, B. N., 5, 43 complex intermetallics, 202 Delone set, 5 concho-spiral, 110 Democritus, 1 confusion principle, 205 dense random packing, 65

Index 233

De Rerum Natura, 1 Fischer, W., 44 Descartes, R., 6 Fischer, W. et al.,44 Design in Nature,110 Fischer, W. & Koch, E., 44, 169, 170, 171, 177 diamond net, 135, 136, 149 fivefold symmetry, 18 diblock copolymers, 162 five elements, 1 diffraction, 4, 5, 187, 192, 198 five-rings, 102 Dirichlet, G. L., 42 fixed point symmetries, 34 Dirichlet region, 42, 112, 122, 125 flat point, 172 disclination, 46, 71, 205 flowsnake, 83 disclination networks, 108, 144 fluorite, 194 disheptahedron, 191 Fogden, A., 172 disulphide nanotube, 121 Fogden, A. et al., 174 divine proportion, 21 Fogden, A. & Haeberlein, M., 172 DNA, 6 Fogden, A. & Hyde, S. T., 175 D net, 135, 149, 154, 157, 158 Fowler, P. W. & Tarnai, T., 71 dodecahedron, 201 FRACTINT, 78 double diamond surface, 186 fractal curves, 78 double diamond, 164, 187 Frank, F. C., 198, 203, 204 double gyroid, 189 Frank, F. C. & Kasper, J. S., 45, 202, 204 double icosahedron, 90, 113 Frank-Kasper phases, 45, 46, 99, 145, 202 doubly-periodic, 9, 14 Frank-Kasper polyhedra, 204, 205, 208 Doye, J. P. K & Wales, D. J., 109 FRD, 168 dragon curve, 79, 80, 81, 82 Friauf-Laves phases 41, 45, 145 Dress, A. W. M., 146 Friauf polyhedron, 41, 99 D surface, 165, 171, 184 fullerenes, 29, 30, 109 dual configuration, 42 fundamental patch, 172 duality, 26 fundamental region, 11, 176 Duhem, P., 6 Duneau, M. & Audier, M., 76 -brass, 95, 97, 98 Dunlap, R. A., 21, 22 -unit, 156, 157 Dürer, A., 10, 11, 24, 199 Gardner, M., 16, 55 Dürer’s pentagonal tiling, 11 Gauss, C. F., 4 Du Val, P., 118 Gauss-Bonnet theorem, 28 Dyer, A., 137 Gaussian curvature, 4, 28, 172 Gauss map, 172, 173 Elam, K., 22 generalised crystallography, 5, 199 electronegativity, 193 generating patch, 165, 169 electron microscopy, 6 genus, 181, 189 El-Said, I. & Parman, A., 10 geodesics, 163, 171 Elser, V., 179, 180, 181 geometry, Elser, V. & Henley, C. L., 57 differential, 162 Epicurus, 1 hyperbolic, 4, 175, 183 equal area mapping, 120 non-Euclidean, 3 equiangular spiral, 110 Riemannian, 4 equipotential surfaces, 187 Geometrical Foundations of Natural Structure, 7 Erickson, R. O., 117 G-H pair, 14, 169 Euclid, 3 Ghyka, M., 22, 110 Euclidean transformation, 112 Gleiter, H., 206 Euler, L., 6, 197 Godel, K., 6 Euler characteristic, 27, 182 Goetzke, K. & Klein, H.-J., 136, 172 golden mean, 203 faujasite, 134 golden number, 21, 55 Fedorov, E. S., 4, 43 golden spiral, 124, 131 Fedorov’s parallelohedra, 43, 145 golf balls, 70 Fejes Tóth, L., 20, 68 Gotoh, K. & Finney, J. L., 67 Ferey, G., 161 Gozdz, W & Holyst, R., 162, 188 Ferro, A. C. & Fortes, M. A., 145 grain boundary, 71 Feynman, R., 206 graphite, 31 Fibonacci numbers, 203 graphite layers, 119 Fibonacci sequence, 21, 122, 123 Grünbaum, B., 40 Fibonacci spiral, 124, 125 Grünbaum & Shephard, 7, 16, 18, 20, 23 field-ion micrograph, 192 Gummelt, P., 18, 20, 200

234 Index

Gummelt, P. & Bandt, C. A., 20 hypercube, 55 Gummelt’s decagon, 20, 21, 200 hypersphere, 4 gyroid, 134, 168, 174, 175, 176, 177 i3 unit, 89, 103 HAADF, 192 i13 supercluster, 90, 102 Haeckel, E., 13 ice XII, 141, 143 Haeckelite, 13 icosahedral symmetry, 25, 197 Hägg, G., 195 icosahedron, 55 Hägg phases, 195, 196 icosahelix, 112, 115 Hahn, J. T., 32, 50, 172 Iijima, S., 119 Hales, T. C., 61, 107, 191 infinite polyhedra, 132, 133, 134, 153, 154 Hamada, N. et al., 119 inflation rules, 84, 86 Hamilton, W. R., 118 Inoue, 204, 205, 207 Hamkins, J. & Zeger, K., 68 interatomic bonds, 193 Han, S. & Smith, J. V., 142 intermetallics, 194 Hargittai, I., 21, 123, 128 International Tables for Crystallography, 32, 50, 172 Hargittai, M., 127 International Union of Crystallography, 201 Harmonice Mundi, 2 International Zeolite Association, 139 Harrison, W. A., 187 interwoven nets, 149, 150 Hart, G. W. & Picciotto, H., 107 interstitial compounds, 196 Haüssermann, U. et al., 159 interwoven nets, 149, 176 hcp, 191 Introduction to Geometry, 122, 124, 122, 125 Heesch, H. & Laves, F., 62, 151 I-WP, 167, 168 Heisenberg, W., 6 helical structures, 110, 198, 207 jammed packings, 59, 60 helicoid, 162, 163 Janot, Ch. & Patera, J., 21 helix, 110 Jeanneret, C. E. (‘le Corbusier’) 22 Hellner, E. & Koch, E., 161, 203 Jeong H.-C., 21 heptagons, 13, 31, 142 Jeong H.-C. & Steinhardt, P. J., 20 Herman–Mauguin symbols, 32 jitterbug, 72 Herz-Fischler, R. A., 21 Johnson, C. K. et al., 12, 51 hexagonal close packing, 191 Johnson, R. L., 107 hexagonal symmetry, 6 Jovanovic, R., 123, 124 hierarchical structure, 6, 22, 19, 77, 198 higher dimensional sphere packing, 67 kagome, 10, 18, 55, 59, 144 Higgins, J. B., 136 Kapraff, J., 126 Hilbert, D., 191 Karcher, H., 164 Hilbert’s curve, 78, 79, 80 Karcher, H. & Polthier, K., 172, 173 Hipparchus, 4 Katz, A., 55 Hiraga, K., 200 Kelvin, W. T. & Weaire, D., 36 Hiraga, K. et al., 90, 95, 200 Kelvin polyhedron, 36,149 Hoare, M. R. & Pal, P., 107 Kepler, J. 6, 7, 8, 11, 24, 25, 59, 61, 87, 107, 190, Hobbs et al., 136, 138 199 Hoffman, D., 164 Kepler (snowflake), 59 Hooke, R., 6 Kepler’s tilings, 10, 13, 59 Hren, J. J. & Ranganathan, S., 192 Kepler-Poinsot polyhedra, 25 Hsiang, W. Y. & Hsiang, W.-Y., 61 Kikuchi, R., 23 H surface, 167 Klinowski, J. et al., 162 Hudson, D. R., 75 Koch, E., 177 Hume-Rothery, W., 194, 195 Koch, E. & Fischer, W., 49, 63, 64, 169, 172, 177, 178 Hume-Rothery phases, 194 Koch’s snowflake curve, 81, 82 Huntley, H. E., 22 Komura, Y. et al., 94 Huson, D. H., 149 Kottwitz, D. A., 68 Hyde, S. T., ix, 163, 174, 175, 182 Kovacs, F. & Tarnai, T., 72 Hyde S. T. & Andersson, S., 163, 182 Kowalewski, 56, 198 Hyde, S. T. & Ramsden, S., 12, 149, 162, 175, 176, Kowalewski units, 56, 58, 199 177, 182 Kramer, P., 67, 87, 198 Hyde, S. T. et al., 162, 186 Kramer, P. & Neri, R., 199 hydrate, 137 Kramer’s hierarchical tiling, 87, 198 hydrocarbons, 138 Kramer, P. & Neri, R., 18 , 55 hyperbolic plane, 175 Kreiner, G. & Franzen, H. F., 88, 89, 90, 100, 157, 203 hyperbolic space, 3 Kreiner, G. & Schäpers, M., 89, 100

Index 235

Kripyakevich, P. I., 42, 194 Mackay, A. L. & Terrones, H., 182 Kuijlaars, A. B. J. & Saff, E. B., 70 Mackay, A. L. et al., 68, 162, 172 Kuo, K. H. A., 100 Mackay, R., 19 Mackay cluster, 91, 95, 96 -Al4Cr, 203 Mackay icosahedron, 96, 102, 203 labyrinth, 165, 167, 168, 176, 178, 179, 184 Mackintosh, A. R., 187 labyrinth graph, 153, 164, 177 magic numbers, 108 LAGEOS, 69 Mandelbrot, B., 77 Latham, R.E., 1 Manoharan, V. N. et al., 109 Lambert, L. et al., 188 Margulis, L. et al., 121 lattice, 9, 32 Marzec, C. & Kapraff, J., 126 Bravais, 32 Mathematica, 187, 209 face-centred cubic (fcc), 37, 38, 191, 192, 195, matching rule, 16 196, 197, 206 Maxwell, J. C., 6 lattice complex, 44 Micrographia, 7, 8 Laplace, P.-S., 162 Mìch, R. & Prusinkiewicz, P., 78 Laves phase, 41, 45, 74, 194, 202 Meier, W. M. & Moeck, H. J., 136 Lavoisier, A., 3 Melnyk, T. W. et al., 71 Leech, J., 72 Mendeleev number, 196 Lehninger, L. et al., 118 Menelaus, 4 Lennard-Jones potential, 107 Mercury (software), 210 Leonardo da Vinci, 22 metallic bond, 190 Leoni, S. & Nesper, R., 188 metallic glasses, 75, 204 level surfaces, 187 methane, 138 Levine, D., 55 Meusnier, J.-B., 162 Levine, D. & Steinhardt, P. J., 199 Mg32 (Al, Zn)49, 42 Li, C. R. et al., 128, 207 Mg3Cr2Al18, 156, 157, 158 Li, H. et al., 160 Mg–Zn–Sm, 203 Liber Abaci, 22 micrograph, 200 Lidin, S., 173 Mikalkovic, M. et al.,56 Lidin, S. & Andersson, S., 112 Miller-Bravais indices, 203 Lidin, S. & Larsson, S., 174 mineralogy, 201 Lidin, S. et al., 168 minimal area foam, 208 Liebau, F. et al., 137 minimal circuits, 145 Lifschitz, R., 15 minimal surfaces, 162 Lidin, S., 173 orthorhombic, 173, 174 Lidin, S. & Andersson, S., 111 rhombohedral, 173, 175 Lidin, S. & Larsson, S., 174 tetragonal, 173 Lindenmayer, A., 77 Miracle, D. B., 68, 75, 206 Lindenmayer systems, 77 Miracle D. B. et al., 75 Livio, M., 21 Miyazaki, K., 58 Lobachevski, N. I., 3 Miyazaki, K. & Takada, I., 58 Loeb, A. L., 42 Miyazaki, K. & Yamagiwa, T., 58 logarithmic spiral, 110 module, 50, 40 Longuet-Higgins, M. S., 56 modular structure, 51, 55, 77 lonsdalite, 137, 141 MOF-14, 160 Lord, E. A., 16, 21, 50, 11, 113, 120, 170, 172, 182, Molnár, E., 166 207 monohedral tiling, 14, 146, 148 Lord, E. A. & Mackay, A. L., 172, 185 Moore, A. J. W. & Ranganathan, S. 192 Lord, E. A. & Ranganathan, S., 21, 65, 103, 104, Mueller, E. W. & Tsong, T. T., 192 111, 119, 200, 207 multigrid, 199 Lord, E. A. & Wilson, C. B., 162 multiple catenoid, 169, 170 Lord, E. A. et al., 86, 106, 200, 202 Mysterium Cosmographicum, 8 Louzguine, D. et al., 207 low density sphere packings, 62 nanocrystals, 206, 207 L-systems, 77 nanoquasicrystals, 207 Lück, R., 11 nanotubes, 119, 120 Lucretius, 1 Nath, M. & Rao, C. N. R., 121 L-unit, 90, 102, 103, 158 Naylor, M., 125, 126 NaZn13, 159, 160 -Al4Mn, 203 NbO, 151, 166 Mackay, A. L., 6, 19, 55, 56, 95, 104, 107, 199, 203 n-colour pattern, 14

236 Index

Nelson, D. R. & Spaepen, F., 47, 194 perovskite, 41 neolithic stone balls, 2, 3 Petrie, J. F., 132 Neovius, E. R., 167 Petrie polygon, 153, 164, 167, 185 Nesper, R., 194 Pettifor, D., 196 Nesper, R. & Leoni, S., 189 Pettigrew, J. B., 110 nested polyhedra, 7, 95, 196 Phillips, E. G., 32 nets, 9, 62, 132 phyllotaxis, 121 Nitsche, J. C. C., 162 Photoshop, 210 nodal surfaces, 187 pineapple, 112, 124 non-Euclidean geometry, 3, 4 pine cone, 123 non-orientable, 177 Pisano, L. (‘Fibonacci’), 22 nucleons, 108 Plateau, J. A. F., 162 Nyman, H. & Anderssen, S., 97, 155, 156, 161 Plateau’s problem, 162, 186 Nyman, H. & Hyde, B. G., 161, 203 platinum, 192 Nyman, H. et al., 114, 155 Plato, 1 Platonic solids, 2, 24, 44, 190 Oberteuffer, J. A. & Ibers, J. A., 99 Poincaré representation, 175 oblate unit, 86 Poinsot, L., 25 octahelix, 112 point groups, 34, 110, 191, 201 OCTO, 167 polygonal helix, 64, 111, 112 Ogawa, T., 85 polyhedral nets, 153, 154 Oguey, C. & Sadoc, J.-F., 175 polymorphism, 192 O’Keeffe, M., 76, 136, 141, 146, 148, 153 polynet, 153, 154, 156, 159 O’Keeffe, M. & Brese, N. E., 136, 140 polytetrahedral structures, 45–47, 46, 107 O’Keeffe, M. & Hyde, S. T., 9, 60, 136 polytope {3, 3, 5}, 47, 118, 144, 207 O’Keeffe, M. et al., 76, 153 Povray, 210 On Growth and Form, 6, 110, 123 PowerBasic, 210 OpenOfﬁce, 210 Priestley, J., 3 orbifold, 12, 51 projection, 55 Osserman, R., 162 prolate unit, 86 Ozin, G. A., 162 protein helices, 118, 207 Prusinkiewicz, P. & Lindenmayer, A., 77, 78 Pacioli, L., 21, 22 pseudobatwing, 52 packing P surface, 161, 166, 171, 174, 184 of circles, 59 Ptolemy, 4 of circles in a circle, 61 Pt3O4, 160, 161 of polyhedra, 35, 208 PtS, 151 of rods, 76 pure metals, 191 of spheres, 62, 190, 199, 207 pyrochlore, 154, 155, 157, 158 cubic close packing (ccp), 191 pyrochlore unit, 103, 154 hexagonal close packing (hcp), 191 of unequal spheres, 73 quasicrystals, 6, 197 low density, 62 quasiperiodicity, 199 random, 65, 205 quasi-simple nets, 148 on a spherical surface, 68, 128 quasi unit cell, 103 Paint Shop Pro, 210 quaternions, 118 palladium, 206, 207 parallelohedron, 146, 148 Rakhmanov, E. A. et al., 70, 128 Paris Academy of Science, 3 Ramachandra Rao, P. & Sastry, G. V. S., 202 Pauling, L., 73, 88, 97, 108, 138, 141, 193, 194, 202 random tiling, 23 Pauling, L. & Marsh, R. E., 48 Ranganathan, S. et al., 194, 197, 203, 206 Pauling triacontahedron, 91 Rao, C. N. R. & Gopalakrishnan, J., 191 Peano, G., 81 rational approximants, 203 Pearce, P., 7, 36, 48, 99, 107, 111, 184, 185 regular polygons, 10 Pearce cluster, 99 rhombic dodecahedron, 26, 57, 58, 186 Peitgen, H.-O. & Richter, P., 77 rhombic icosahedron, 86 Penrose, R., 11, 16, 18 rhombic triacontahedron, 26, 56, 57, 58, 86, 201 Penrose tiling, 7, 11, 16, 17, 77, 199 rhombus tiling, 85 3D Penrose tiling, 85, 86 rings, 133, 135, 136, 145 pentagonal dodecahedron, 47, 48 Rivier, N. 50 pentagrid, 18 Robinson, R. M., 68, 69 periodic tetrahelix, 114 rod packings, 76

Index 237

Rogers, C. A., 191 space filling by regular and semiregular polyhedra, Romeu, D. & Aragon, J. L., 94 36–41 R-phase, 94, 95, 105, 202 space-filling polyhedra, 146 Runnels, L. K., 140 space groups, 4, 5, 32, 50, 191, 197 Spheraeca, 4 saddle polyhedra, 135, 152, 171, 181, 182, 184, sphere packing, 199 185 spherical crystal, 71 Sadoc, J. F. 207 spherical tiling, 23, 24 Sadoc, J. F. & Charvolin, J., 175 spiral distribution on a spherical surface, 127, 128, Sadoc, J. F. & Mosseri, R., 36, 47, 68, 100, 119, 145, 130 194, 207 spiral structures, 110 Sadoc, J. F. & Rivier, N., 65, 117, 118, 207 spiral phyllotaxis, 121, 123 Samson, S., 89, 93, 99, 193 stacking faults, 101 Samson cluster, 93 stacking sequence, 102 Sander, L. M., 77 star polygons, 25 saw chain, 141, 142 star polyhedron, 56, 86 Schattschneider, D., 9, 14 Steinhardt, P. J. & Ostlund, S., 18, 55, 56 Shechtman, D. et al., 197 Steinhardt, P. J. et al., 103, 198, 200 Schechtmanite, 91 stella octangula, 108 Scheffer M. & Lück, R., 15 stella quadrangula, 97, 155, 159 Scherk, H. F., 164 stellated polyhedra, 87 Scherk’s surfaces, 164 Stessmann, B., 177 Schindler, M. et al., 159 Steurer, W., 191 Schlegel diagram, 146 Steurer, W., et al., 105 Schoen, A. H., 167, 172, 183 Stewart, I., 70 Schoen’s batwing, 52 Stone, A. J. & Wales, D. J., 13 Schoen’s surfaces, 167 Stone-Wales defect, 13, 14 Schoenflies, A., 4, 166 structure factors, 187, 189 Schrandt, R. G. & Ulam, S., 77 Structure in Nature is a Strategy for Design, 7 Schrödinger, E. 6 Sugiyama, K. et al., 98 Schubnikov, A. V. & Belov, N. V., 15 Sullinger, D. B. & Kennard, C. H. L., 42, 88 Schwarz, H.A., 164 sunflower, 123 Schwarzite, 28, 29 Surface Evolver, x, 172, 210 Schwarz’s H surface, 149 Sutton, D., 24 Schwarz, U. S. & Gompper, G., 187, 189 Swinton, J., 128 Scott G. D. & Kilgour, D. M., 66, 67 symmetry group, 9, 12 screw axes, 110 Székely, E., 69, 128 screw transformation, 113 Seifert, G. et al., 121 T2 phase, 105 secondary building unit (SBU), 139 Tait, P. G., 118 self-intersection, 177 Takakura, H. et al., 98 self-similarity, 110 Tammes, P. M. L., 68 semi-regular polyhedra, 6, 24 Tammes problem, 68 Sendai, 204 Tarnai, T., 60, 70 Senechal, M., 5 Tarnai, T. & Gáspár, Zs., 69 Senechal, M. & Fleck, G., 153 Tanaka, K. et al., 119 Senkov, O. N. & Miracle, D. B., 75 Tenne, R. et al., 121 shape grammars, 77 TEM, 192 Sheng, H. W., et al., 206 Teo, B. K. & Zhang, H., 90 Shukla, K. S., 190 Terrones, H. & Terrones, M., 13, 28, 120, 121 silicates, 136 Terrones, H. et al., 121 Shipman, P. D. & Newell, A. C., 128 tessellation, 9 Skilling, J., 26 tetrahelix, 64 Sloane, N. J. A., 61 Thompson, D. W., 6, 110 Sloane, N. J. A. et al., 68, 109 Thomson, W. (Lord Kelvin), 6, 36 Smalley, R. E. & Curl, R. F., 29 Three dimensional nets and polyhedra, 134 Smith, C. S., 16 Ti2Ni, 156, 203 snowflake, 59, 190 tiling snub cube, 160 aperiodic, 16 sodalite, 132, 138 two-dimensional, 9 solid solutions, 194 random, 23 Solid View, 210 spherical, 23, 24

238 Index

tiling (contd) W3Fe3C, 155 of triply periodic surfaces, 181 Wachman, A. et al., 133 of the hyperbolic plane, 183 wallpaper groups, 9 Tilings and Patterns, 23 Walter, A., 113 topology, 4; Watson R. E. & Weinert, M., 194 of plane tilings, 13, 27 weaving pattern, 18, 19, 52, 53, 54, 55 topological classiﬁcation of tilings, 145 Weaire D. & Phelan, R., 50, 208 topological invariants, 133 Weaire, D. & Rivier, N., 23 topological symmetry group (TSG), 132 Wefelmeier, W. Z., 66 Torquato, S. & Stillinger, F. H., 59 Weierstrass, 163 Torquato, S. et al., 67 Weierstrass function, 163, 172 Townsend, S. J. et al., 182 Wells, A. F., 63, 134, 153, 182 TPMBS, 168 Wells’ {3, 7}, 154 transitive, 27 Wells’ 6.82, 152 translations, 9 Wells’ (8, 3)c, 142, 150 triacontahedra, 106 Wells’ (10, 3)a, 63, 136, 144, 150, 185 triangulated cylindrical polyhedra (TCP), 117 Wells’ (10, 3)b, 135 triangulated helical polyhedron (THP), 117 Wenninger, M., 26, 87 trihedron, 184 What is Life?, 6 triple periodicity, 5 Whyte, L. L. et al., 77 triply-periodic surface, 52, 162 WI-00, 178 Truchet, S., 15 WI-10, 179 Truchet tiling, 15 Williams, R., 7, 36, 48, 183 truncation, 26, 151, 160, 161 Wills, J. M., 67 truncated octahedron, 36, 44 Wilson, C. G. et al., 10 truncated tetrahedron, 45 Wohlgemuth, M., et al., 188 Tsai, a. P. et al., 202 Woods, H. J., 14 Turing, A., 128 wurzite, 137, 141 Turnbull, D., 204 turtle graphics, 78 X-ray diffraction, 4, 5

Ulam, S., 77 Yang, Q.-B. and Anderson, S., 100 uniform nets, 134 unit cell, 9, 12, 32 zeolites, 136, 137, 139 Universal Node System, 107, 184 CAN, 141, 142 Unterweysung der Messung, 24, 25 FAU, 133, 139, 153 FER, 142, 143 van Schuylenburch, 53 LTA (zeolite-A), 132, 133, 139, 153 Venkataraman, G. et al., 194 MFI (ZSM-5), 140 vertex-connected tetrahedra, 136 MTT, 140 vertex ﬁgure, 132 OFF, 142, 143 vertex symbol, 136 STT, 140 Villars, P. & Calvert, L. D., 194 Zhang, Z. et al. 202 Voderberg, H., 20 zigzag, 142 Voderberg spiral tiling, 20 zinc blende, 75, 153 von Laue, M., 4 Zintl phases, 194, 195 von Schnering, H. G. & Nesper, R., 162, 188 Zometool, 107 von Schnering, H. G. et al., 189 zonohedra, 43 Voronoi region, 42, 47, 49, 50, 206 Zr4Al3, 49, 50