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 © 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 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 © 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 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.