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Coxeter H. Ч Regular polytopes
Coxeter H. Ч Regular polytopes



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Ќазвание: Regular polytopes

јвтор: Coxeter H.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1948

 оличество страниц: 346

ƒобавлена в каталог: 24.02.2013

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ѕредметный указатель
$a$-form      175Ч178
$d_{p, q, r}$      273 (see also Density)
$d_{p, q}$      102Ч105
$d_{p}$      94
$g_{p, q}$      82 91
$g_{p, q}$, $g_{p, q, ..., u}$      130Ч133 141Ч144 149 153 232 290
$h$      15 19 61 67 73 91 102 108Ч109 221 225Ч234 243 278
$hH_{n}$      155 201
$k$-chain and $k$-circuit      167 168Ч171
$N_{1}$, $N_{01}$, etc      12 132
$z^{1}, z^{2}, ...$      176Ч178 183Ч185 190 193Ч194 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}      121Ч122 129 136 149 244 254 292
24-cell      3 4 3 148Ч154 245Ч247 270Ч272 289 292
600-cell {3, 3, 5}      153 157 163 167 239 247Ч249 260 270Ч272 292
Ab$\hat{u}$Тl Waf$\hat{a}$      73
Abbott, E. A.      119 236
Abel, N. H.      55 311
Abstract group      41 43 80
Acute rhombohedron      26
Adjoint      177
Affine coordinates      180Ч184 189 213 218Ч219
Affine coordinates, geometry      27Ч28
Alexandroff, A. D.      28
Algebra      167Ч178
Alice through the looking-glass      75
Alternating group      43 48 106
Alternation      11 154Ч156 201
Analogy      118Ч124
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      168Ч171
Br$\ddot{u}$ckner, Max      16 21 26 31 74 115 117 240
Bradwardinus      114
Brahana, H. R.      11
Branch of a graph      6
Brauer, Richard      xi 262
Bravais, Auguste      44 56
Bredwardin      114
Brewster, Sir David      92
Burckhardt, J. J.      xi 28 56 205
Burnside, William      164 210
Calculus, integral      xi 125 144
Cartan, $\acute{E}$lie      209 211Ч212
Cartesian coordinates      2 3 52Ч53 63 70 119 122 127 133 156Ч158 205 214Ч216 239Ч240 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 225Ч226 234 238 274Ч275
Centre      2 130
Ces$\dot{a}$ro, Ernesto      128 132 144 148 150 162
Ces$\dot{a}$ro, Giuseppe (E.Тs brother)      74
Chain      167Ч171
Characteristic equation      214Ч216 219Ч221 225
Characteristic equation, root      214Ч216 220
Characteristic equation, simplex      137Ч141 199
Characteristic equation, tetrahedron      71 282Ч287 290
Characteristic equation, triangle      24 31 66 109Ч111 290
Characteristic equation, vector      214Ч216
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 150Ч151
Collineation      213
Colunar triangles      112
Commutative law      39
complex numbers      3 64 214Ч216
Compound      47 60Ч61 95Ч100 149Ч150 268Ч272 287Ч288 305
Cone      255
Configuration      12 130 210Ч211
Congruent transformation      33 213Ч218
conjugate      42 81 85Ч86 208
Connected form      175
Connected graph      6
Connectivity      9
Content      123Ч127 141 161 183 273 293 295
Continued fraction      134 160
Continuous group      44 204 211Ч212
Contravariant      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 209Ч211 234 262 263 270 286Ч288
Crosby, W. J. R.      185 274
cross      121 251
Cross polytope $\beta_{n}$      121Ч122 129 136 145 149 225 244 245 254 294
Crystal      ix 13 31 74
Crystal, classes      56
Crystal, twin      56
Crystallographic restriction      63
Crystallographic restriction, solids      289
Cube $\gamma_{3}$ = {4, 3}      5 152 236 298
Cubic honeycomb $\delta_{n+1}$      123 136 145 156 181 296
Cubic honeycomb $\delta_{n+1}$, 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
D$\ddot{u}$rer, Albrecht      13
Decagon {10}, and Decagram {$\frac{10}{3}$}      277
Definite form      173Ч174 184 189 193
Degenerate polyhedron      61
Degenerate polyhedron, polytope      123
Del Pezzo, P.      211
density      94 102Ч105 263 266 273 282Ч287 290
Desargues, Girard      14
Descartes, Ren$\acute{e}$      23 31 59
Determinant, $(j, k)$      160 273
Determinant, Schl$\ddot{a}$fliТs      134 161 199
Dickson, L. E.      164
Digon {2}      4
Dihedral angle      22 61 133 136Ч141 154 273 281Ч284 293 295
Dihedral angle, group $[p]$      46 54 62 77 188 195 222
Dihedral angle, kaleidoscope      76
Dihedron {$p$}      2 12 46 67
Dipyramid      5 121
Direct product      42 44 78 188
Direct product, transformation      33 213
Dirichlet, P. G. L.      142
Discrete      44 76
Disphenoid      15 (see also Rhombic Tetragonal)
Displacement      33 213Ч218
Dodecagon {12}      1 246 287
Dodecagram {$\frac{12}{5}}$}      287
Dodecahedron {5, 3}      ix 6 49Ч53 88 96 100 237 298Ч300 Rhombic)
Donchian, P. S.      xi xix 242Ч243 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
Dunne, J. W.      119 260
DupinТs 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 275Ч278
Equilateral zonohedra      28Ч29
Equivalent points      76
Etruscan dodecahedron      13
Euclid of Megara      ix 1 13 30
Euclidean geometry      119 171 235
Euler, Leonhard      55 166 311
EulerТs formula      9 58 104 114 132 165Ч172 203Ч204 232 263 273
EulerТs function      94
EulerТs theorem on rotations      37
Eutactic star      251Ч257 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 98Ч100 267Ч270 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      49Ч50 98Ч100 303 304
Five tetrahedra      49 98Ч100
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      118Ч123 141 258
Franklin, C. H. H.      29
Free product      75
Frontispiece      243 249 28
Fundamental region      63 76Ч87 188 194Ч197 200 205Ч212 297
G function      40 (see also Bessel Elliptic EulerТs Gamma Hypergeometric Schl
Galois, Evariste      55
Gamma function      125
Garnet      31
Gauss, C. F.      14
Gaussian integers      64 164 211
Generalized kaleidoscope      187Ч212
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 150Ч153 162Ч164 202Ч204 210 211 259
Goursat, Edouard      x 116 209 216 280Ч281 284 286
Graph      6 84Ч88 191Ч202 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 96Ч98 100
Great stellated triacontahedron      102Ч103
Group      41 (see also Abstract Alternating Cyclic Dihedral Icosahedral Infinite Octahedral Orthogonal Polyhedral Rotation Space Symmetric Symmetry Symplectic Tetrahedral Trigonal Unimodular)
Groups generated by reflections      x 196 280 285 297
Ha$\ddot{u}$y, R. J.      63
Hadwiger, H.      251Ч252 261
Haeckel, Ernst      13
Half-measure polytope $h_{\gamma_{n}}$      155Ч156 158
Half-turn      34 36
Hamilton, Sir W. R.      7 14 55 56 309
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 115Ч117 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 171Ч172 264 288 296
Hoppe, Reinholdix      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      47Ч50 98
1 2 3
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