Coxeter H.S.M. — Regular Polytopes :: Электронная библиотека попечительского совета мехмата МГУ

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Coxeter H.S.M. — Regular Polytopes

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Название: Regular Polytopes

Автор: Coxeter H.S.M.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1948

Количество страниц: 321

Добавлена в каталог: 25.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$d_{p,q,r}$       273 (see also “Density”)
$d_{p,q}$       102—105
$d_{p}$       94
$g_{p,q,...w}$       130—133 141—144 149 153 232 290
$g_{p,q}$       82 91
$h\Pi_{n}$       155 201
$N_{1}$ , $N_{01}$ , etc.      12 132
$z^{1}$ , $z^{2}$ ,...      176—178 183—185 190 193—194 205 208 212
$\nu_{0}$ , $\nu_{1}$ , etc.      58 291
$\tau$       22
$_{0}R$ , $_{1}R$ , etc.      see “Radii”
120-cell {5,3,3}      153 157 162 240 269 292
16-cell $\beta_{4}$ ={3,3,4}      121—122 129 136 149 244 254 292
24-cell {3,4,3}      148—154 245—247 270—272 289 292
600-cell {3,3,5}      153 157 163 167 239 247—249 200 270—272 292
a-form      175—178
Abbott, E.A.      119 236
Abel, N.H.      55 311
Abstract group      41 43 80
Abu’l Wafa      73
Acute rhombohedron      26
Adjoint      177
Affine coordinates      180—184 189 213 218—219
Affine geometry      27—28
Alexandroff, A.D.      28
Algebra      167—178
Alice through the looking-glass      75
Alternating group      43 48 106
Alternation      11 154—156 201
Analogy      118—124
Analysis situs      14 165
Andreini, Angelo      69 70 74
Angle of a polygon      2 94
Angular deficiency      23
Antiprism      4 5 14 45 255
Apeirogon { $\infty$ }      45 58 296
Apollonius of Perga      30
Archimedean solids      30 117 259
Archimedes of Syracuse      3 30
Area of a polygon      2 3 94
Area of a polyhedral surface      22
Associative law      39
atoms      74
Automorphism      106
Axis of rotation      47 63
Badoureau, A.      73 115
Baker, H.F.      210
Ball, W.W.R.      8 10 14 27 69 92 114 163
Barlow, William      57
Barrau, J.A.      288
Bentley, W.A.      1
Bertrand, J.L.F.      309
Bessel functions      142
Birkhoff, Garrett      38 42 169
Bitangents of a quartic curve      211
Body-centred cubic lattice      74
Boole, George      258
Botany      31
Boundary      167
Bounding k-chain      168—171
Bradwardinus      114
Brahaxa, H.R.      11
Branch of a graph      6
Brauer, Richard      xi 262
Bravais, Auguste      44 56
Bredwardin      114
Brewster, Sir David      92
Brueckner, Max      16 21 26 31 74 115 117 240
Burckhardt, J.J.      xi 28 50 205
Burnside, William      164 210
Calculus, integral      xi 125 144
Cartan, Elie      209 211—212
Cartesian coordinates      2 3 52—53 63 70 119 122 127 133 156—158 205 214—216 239—240 245—247
Catalan, E.C.      259
Cauchy, A.L.      55 72 114 116 309
Cayley numbers      211
Cayley, Arthur      14 56 115 116 141 172 309
cell      68 120 127 197
Cell-regular compound      272
Central symmetry      27 91 225—226 234 238 274—275
Centre      2 130
Cesaro, Ernesto      128 132 144 148 150 162
Cesaro, Giuseppe (Ernesto’s brother)      74
Chain      167—171
Characteristic equation      214—216 219—221 225
Characteristic root      214—216 220
Characteristic simplex      137—141 199
Characteristic tetrahedron      71 282—287 290
Characteristic triangle      24 31 66 109—111 290
Characteristic vector      214—216
Chasles, Michel      55
Chebyshev, P.L.      222
Chess board      50
Chlorine      74
Chrome alum      13
Circogonia and Circorrhegma      13
Circuit      166 168
Circum-circle      2
Circum-radius      3 21 133 158 161
Circum-sphere      16
Clifford, W.K.      217 239
Close-packing      70
Coherent indexing      51 59 150—151
Collineation      213
Colunar triangles      112
Commutative law      39
complex numbers      3 64 214—216
Compound      47 60—61 95—100 149—150 268—272 287—288 305
Cone      255
Configuration      12 130 210—211
Congruent transformation      33 213—218
conjugate      42 81 85—86 208
Connected form      175
Connected graph      6
Connectivity      9
Content      123—127 141 161 183 273 293 295
Continued fraction      134 160
Continuous group      44 204 211—212
Contra variant      179
Convex      4 126
coordinates      see “Affine” “Cartesian” “Normal” “Oblique” “Quadriplanar” “Tangential” “Trilinear”
copper      74
Core      98
Coset      42
Courant, Richard      143
Covariant basis      178
Covariant component      179
Coxeter, H.S.M.      30 32 52 92 97 109 117 142 162 164 199 203 209—211 234 262 263 270 286—288
Crosby, W.J.R.      185 274
cross      121 251
Cross polytope $\beta_{n}$       121—122 129 136 145 149 225 244 245 254 294
Crystal      ix 13 31 74
Crystal classes      56
Crystal twin      56
Crystallographic restriction      63
Crystallographic solids      289
Cube $\gamma_{3}$ ={4,3}      5 152 236 298
Cubic honeycomb $\delta_{n+1}$       123 136 145 156 181 296
Cubic surface      142 211
Cuboctahedron      18 52 69 152 298 299
Curie, Pierre      57
Curjel, H.W.      144
CYCLE      40
Cyclic group      41 43 54 62 77
Cyclotomy      3 14
Decagon {10}, and Decagram { $\frac{10}{3}$ }      277
Definite form      173—174 184 189 193
Degenerate polyhedron      61
Degenerate polytope      123
Del Pezzo, P.      211

density      94 102—105 263 266 273 282—287 290
Desargues, Girard      14
Descartes, Rene      23 31 59
Determinant, (j,k)      160 273
Determinant, Schlaefli’s      134 161 199
Dicksox, L.E.      164
Digon {2}      4
Dihedral angle      22 61 133 136—141 154 273 281—284 293 295
Dihedral group [p]      46 54 62 77 188 195 222
Dihedral kaleidoscope      76
Dihedron {p,2}      12 46 67
Dipyramid      5 121
Direct product      42 44 78 188
Direct transformation      33 213
Dirichlet, P.G.L.      142
Discrete      44 76
Disphenoid      15 (see also “Rhombic” “Tetragonal”)
Displacement      33 213—218
Dodecagon {12}      1 246 287
Dodecagram { $\frac{12}{5}$ }      287
Dodecahedron {5,3}      ix 6 49—53 88 96 100 237 298—300 “Rhombic”)
Donchian, P.S.      xi xix 242—243 260 262
Donkin, W.F.      55
Donnay, J.D.H.      xi 37
Double rotation      216 221 229 233
Dreams, prophetic      260
Du Val, Patrick      32 56 97 116 117 185 211 212
Dual maps      6 60
Dudeney, H.E.      14
Duerer, Albrecht      13
Dunne, J.W.      119 260
Dupin’s indicatrix      15
Dyck, Walther      92
EDGE      4 120 127
Einstein, Albert      186
Elements $\Pi_{j}$       68 70 127 197
Elements, the four      13
Elliptic functions      62
Elliptic geometry      217
Elongated dodecahedron      20 257
Elte, E.L.      164 210
Enantiomorphous      33 141 213
Enneagon {9}      1
Equator      67 73
Equatorial polygon {h}      18 90 275—278
Equilateral zonohedra      28—29
Equivalent points      76
Etruscan dodecahedron      13
Euclid of Megara      ix 1 13 30
Euclidean geometry      119 171 235
Euler, Leonhard      55 166 311
Euler’s formula      9 58 104 114 132 165—172 203—204 232 263 273
Euler’s function      94
Euler’s theorem on rotations      37
Eutactic star      251—257 261
Even face      7
Even permutation      40 49
Ewald, P.P.      181
Existence of star polytopes      282
Expansion and contraction      210
Extended polyhedral groups      82
Face      4 127 “Odd”)
Face-centred cubic lattice      74
Face-regular compound      47
Faceting      95 98—100 267—270 302—304
Factor group      43
Fedorov, E.S.      31 57 74 257
Fermat, Pierre de      14
Fibonacci numbers      23 31
Finite differences      258
Five cubes      49 100 240
Five octahedra      49—50 98—100 303 304
Five tetrahedra      49 98—100
Flather, H.T.      32 97 117
Flatland      98 119 236
Forchhammer, G.      144 165
Ford, L.R.      56 105
Forder, H.G.      xi
Forest      6
FORM      see “Quadratic”
Four-colour problem      14
Fourth dimension      118—123 141 258
Franklin, C.H.H.      29
Free product      75
Frontispiece      243 249 286
Function      40 (see also “Bessel” “Elliptic” “Euler’s” “Gamma” “Hypergeometric” “Schlaefli”)
Fundamental region      63 76—87 188 194—197 200 205—212 297
Galois, Evariste      55
Gamma function      125
Garnet      31
Gauss, C.F.      14
Gaussian integers      64 164 211
Generalized kaleidoscope      187—212
Generalized kaleidoscope, Petrie polygon      91 223
Generating relations      41 75 77 80 188
Generators      41
Genus      10 105
Gergonne, J.D.      73
Glaisher, J.W.L.      164
Glide-reflection      36 37 221
Gogh, Vincent van      143
Gold      74
Golden section      30 52 162
Gordan, P.A.      109 116 274
Gosset, Thorold      x xi 144 150—153 162—164 202—204 210 211 259
Goursat, Edouard      x 116 209 216 280—281 284 286
Graph      6 84—88 191—202 280—285
Grassmann, Robert      141
Great dodecahedron {5, $\frac{5}{2}$ }, Great icosahedron {3, $\frac{5}{2}$ }, and Great stellated dodecahedron { $\frac{5}{2}$ ,3}      96—98 100
Great stellated triacontahedron      102—103
Group      41 (see also “Abstract” “Alternating” “Cyclic” “Dihedral” “Icosahedral” “Infinite” “Octahedral” “Orthogonal” “Polyhedral” “Rotation” “Space” “Symmetric” “Symmetry” “Symplectic” “Tetrahedral” “Trigonal” “Unimodular”)
Groups generated bv reflections      x 196 280 285 297
H      15 19 61 67 73 91 102 108—109 221 225—234 243 278
Hadwiger, H.      251—252 261
Haeckel, Ernst      13
Half-measure polytope $h\gamma_{n}$       155—156 158
Half-turn      34 36
Hamilton, Sir W.R.      7 14 55 56 309
Hauey, R.J.      63
Haussner, Robert      94 96 114
Heath, Sir T.L.      13 30 92 114 115
Heawood, P.J.      14
Hedrick, E.R.      310
Helical polygon      45 91
Heptagon {7}      114
Hermes, Oswald      14
Heron of Alexandria      30
Herschel, A.S.      8
Hess, Edmund      x 31 56 73 74 92 115—117 263 286 287
Hessel, J.F.C.      57 116 286
Hessenberg, Gerhard      186
Hexagon {6}      1 277
Hilton, Harold      37
Hinton, C.H.      119 236 258
Hinton, James      258
Hirsch, Meier      31
Honeycomb      58 68 122 127 171—172 264 288 296
Hoppe, Reinhold      ix 144 165
Houdini, Harry      119
Humphreys, W.J.      1
Hurwitz, Adolf      164
Hyper-cube      118 237
Hyper-sphere      see “Sphere”
Hyperbolic geometry      xi 109 171
Hypergeometric functions      142
Hyperplane      120
Hypsicles      30
Icosagon {20}      287
Icosahedral group      47—50 98
Icosahedron {3,5}      5 52 88 97 117 237 251 298 300

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