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| Ïîèñê ïî óêàçàòåëÿì |
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| Coxeter H.S.M. — Regular Polytopes |
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| Ïðåäìåòíûé óêàçàòåëü |
Icosian game 8
Icosidodecahedron 18 50 53 298 299 303 304
Identity 34 39
Image 75
In-circle 2
In-radius  3 21 161
In-sphere 16 257
Incidence matrix 166—171
Indefinite form 173
Index of a subgroup 42
Indexing see “Coherent”
Indices of a crystal 186
Infeld, Leopold xi 56
Infinite groups 192—196 205
Inner product 178—184
Integral calculus 125 144
Integral Cayley numbers 211
Integral Quaternions 164 211
Intuition 119
Invariant 40 214
Inverse 39
inversion 37 91 225
Iron 74
Irreducible group 188
Isohedral-isogonal polyhedra 116—117
Isometric projection 243
Isomorphic groups 43
Isomorphic polyhedra 106—107
Isomorphic polytopes 265—267 277
Jacobi, C.F.A. 313
Jacobi, C.G.J. 142
Jordan, Camille 55
Jouffret, E.P. 136
k-chain and k-circuit 167 168—171
Kaleidoscope 92 (see also “Dihedral” “Generalized” “Prismatic” “Tetrahedral” “Trihedral”)
Kelvin, Lord 35 37 38
Kempe, A.B. 14
Kepler, Johann 14 29 31 47 56 73 114 310
Kepler-Poinsot polyhedra 96—111 263—265 269
Kinematics of a rigid body 33—55
Klein, Felix vii 12 56 82 92
Koenig, Denes 9
Koenigsberg bridges 14
Kowalewski, Gerhard 26 50
Kronecker, Leopold 174
Lagrange, J.L. 55
Lattice 62 74 122 181 205—207
Leibniz, G.W. 31
Leonardo of Pisa 31
Levi, F.W. 41 43
Lhuilier, S.A.J. 14
Lie, M.S. 211—212 313 314
Line of symmetry 65—68 86
Linear group 212
Linear transformation 213
Lines on the cubic surface 211
Listing, J.B. 14
Lobatschewsky, N.I. ix
Lucas, Edouard 1 8 31 115 135
Luke, Dorman xi
Lyche, R. Tambs 185
MacLane, Saunders 38 42 169
Mahler, Kurt 185
Manning, H.P. x 136 141
MAP 6 58 64 232
Matrix 12 166—171 175 210
Maurolycus of Messina 30
McShane, E.J. 307
Measure polytope  123—124 129 136 145 150 155 239 244 255—258 262 294
Metrical properties 158—162 273 293 295
Mid-sphere 16
Miller, G.A. 56
Miller, J.C.P. xi
Miller, W.H. 186
Minkowski, Hermann 119 185
Mirror 75 83
Mobius, A.F. 14 56 92 116 141
Models 5 242—243 260 262
Moore, E.H. 199
More, Henry 119
Morris, G.G. 310
Murder 56
Music of the Spheres xi 283
Mysticism 119 258
Napier, John 307 314
Nature 13 31
Neper see “Napier”
Net 10 13 236 259
Neville, E.H. xi 118
Niggli, Paul 73
Noble, C.A. 310
Node of a graph 6
Non-existence of star-honeycombs 285
Non-singular star 27
Normal coordinates 183 220
Normalized eutactic star 251—254
Notation 290
Null graph 198
Null polytope  128 166
Nullity 175
Number of elements 13 72 131—132 149 153 267 274 292 294
Number of reflections 68 227
Oblique coordinates 64 182 187 189
Obtuse rhombohedron 26
Octagon {8} 243
Octahedral group 47
Octahedron  ={3,4} 5 50 52 121 150 198 247 250 298—301 304
Odd face 7
Odd permutation 40
Opposite transformation 33 213—216
Order of a group 41 202—209 etc.)
Orthogonal group 212
Orthogonal matrix 288
Orthogonal projection 243—262
Orthogonal transformation 213—221 261
Orthoscheme 137—143 199 210 223
Orthotope 123
Oss, S.L. van iv 115 249 260 265 266 274—280 286—287
Pappus Of Alexandria 88 92 238 269
Parallel-sided 2n-gon 28
Parallelohedron 29 257
Parallelotope 122 206
Partial truncation 154—156 201
Pascal, Ernesto 222
Path 80 188
Pentagon {5} 1 3 243
Pentagonal dodecahedron see “Dodecahedron {5
Pentagonal polyhedra ix 98 104 107 289
Pentagonal polytopes 266 289
Pentagram { } 93—96 114
Pentatope  ={3,3,3} 120 292
Period 39
Permutation 40 46 49 222 226
Petersen, Julius 14
Petrie polygon 24 61 90—92 102 108 223—230 243—250 270 278—280 286—287 290
Petrie, J.F. 31—32 97 116 117
Petrie, Sir W.M.F. 31
Pezzo, P. del 211
Phyllotaxis 31
Pitsch, Johann 25 115
Plane of symmetry 65 71 73 86 130 226—234
Plates xix 4 32 49 160 176 243 256 273
Plato 13 30
Platonic solids 5 20 116 289 292
Pohlke, Karl 261 313
Poincare, Henri 14 92 118 165—171
Poinsot, Louis 94—97 114 307 309
Polar hyperplane 126
Polar zonohedra 29 256
Polya, George 73 124
| Polygon 1 (see also “Helical” “Petrie” “Regular” “Skew” “Star-polygon”)
Polyhedral groups 47 55
Polyhedron 4 (see also “Isohedral-isogonal” “Kepler-Poinsot” “Platonic” “Quasi-regular” “Regular” “Star-polyhedron”)
Polytope ix 118 126 “Pentagonal” “Regular” “Spherical”)
Positive definite form 173—174 184 189 193
prism 4 123—124 255
Prismatic kaleidoscope 78 190
PRODUCT 38 124 “Free” “Inner “Rectangular” “Vector”)
Projection 236 241—262 “Orthogonal”)
Projective geometry 12 28 211
Puchta, Anton 136 144 164
Pyramid 4 120 123
Pythagoras 16
Pythagoreans ix 13 114
Quadratic form 142 173—179 192 “Definite” “Indefinite” “Semi-definite”)
Quadriplanar coordinates 183
Quadrirectangular tetrahedron 71 84 137—142 282
Quartic curve 211
Quasi-regular honeycomb 69 88
Quasi-regular polyhedron 18 100—101 107
Quasi-regular tessellation 60
Quaternions 164 211
Quotient group 43 205
Rademacher, Hans 31 313
Radii of a polygon 2
Radii of a polyhedron 16 293
Radii of a polytope 130 159 161 273 293 295
Radiolaria 13
Rank of a matrix 169—171 175
Ray 75
Reciprocal honeycombs 70 153 205
Reciprocal lattices 181 207
Reciprocal polygons 94
Reciprocal polyhedra 17 89
Reciprocal polytopes 126 127 140 200 265—266 269—272
Reciprocal properties 17 141 275
Reciprocal tessellations 60
Rectangular product of polytopes 124 202
Recurrence 23 126 134 160
Reducible group 188
Reflection 34 75—92 182 187 213 217—230
Region see “Fundamental”
Regular honeycomb 68 129 136 182 198 296
Regular map 11
Regular polygon 2 45 93 199 “Decagon” “Digon” “Dodecagon” “Enneagon” “Heptagon” “Hexagon” “Icosagon” “Octagon” “Pentagon” “Square” “Triacontagon” “Triangle”)
Regular polyhedron 5 16 199 292 “Dodecahedron” “Icosahedron” “Octahedron” “Tetrahedron”)
Regular polytope 128 136 198 209 292—295 “120-cell” “Measure “Pentatope” “Simplex” “600-cell” “16-cell” “Tessaract” “24-cell”)
Regular tessellation 59 296
Relativity 119
Rhombic disphenoid 15 116
Rhombic dodecahedron 25—26 31 70 256
Rhombic icosahedron 29 256
Rhombic tessellation 60
Rhombic triacontahedron 25—26 49
Rhombicosidodecahedron 117 259 299
Rhombohedron 26
ribbon 230
Ricci, M.M.G. 186
Richelot, F.J. 14
Richmond, H.W. 14 142
Riemann surface 104—105 110
Riemann, Bernhard 14 116
Ring 124 (see also “Torus”)
Robinson, G. de B. xi 92 210 239
Robson, Alan xi
Rodrigues, Olinde 55
Rohrbach, Hans 185
Room, T.G. 211
Rotation 34 47 63 124 187 215—221 224 243 “Double”)
Rotation group 45 53—56 62 108
Rotatory-reflection 37 57 91 221
Rouse Ball, W. W see “Ball”
Rudel, K. 144 165
Ruffini, Paolo 55
Salt 13 74
Scaffolding of a graph 9
Scalar product of vectors 178—184
Schlaefli function 142—144 213 232 234
Schlaefli symbol 14 69 87 116 129 138 146—148 155 275 286
Schlaefli, Ludwig ix x 14 31 114 118 135 136 141—144 162—165 172 211 232—234 251 261—264 285—287 307
Schlegel diagram 10 242
Schlegel, Victor xi 10 144 243
Schoenemann, P. 52
Schoenflies, A. 57
Schoenhardt, E. 306
Schoute, P.H. 16 56 124 141 163 164 205 211 233 235 239 270 287 288
Schubert, Hermann 235
Schur, Friedrich 311
Schwarz, H.A. 56 92 112—113 116 261 280—284 296
Screw-displacement 37
Section 236—240 298—304
Self-conjugate subgroup 42
Self-reciprocal polygon 95
Self-reciprocal polygon, lattice 211
Semi-regular polytope 152 162 210
Semidefinite form 173—178 184 189 192—193
Shadow 236 240—258
Simplex  120—121 129 136 145 225 244 245 250 294 “Spherical”)
Simplicial subdivision 130 138 206 228 229 285
Simplified section 238
Simply-connected 1 9 171
Singular point on a surface 212
Six-dimensional polytope  202—203
Skew polygon 1
Skew polyhedron 32
Small stellated dodecahedron {,5} 96—98 100
Small stellated triacontahedron 102—103
Snowflake 1
Snub 24-cell s{3,4,3} 151—153 157 162—163 166
Sodium atoms 74
Sodium sulphantimoniate 13
Sohncke, L.A. 57
Sommerville, D.M.Y. x xi 9 10 12 15 118 122 124 134—137 166 238
Space groups 57
Space-time 119
Special subgroup 191 205
Speiser, Andreas 73
Sphere 119 125—126 “In-sphere” “Mid-sphere”)
Spherical excess 23
Spherical honeycomb 137—141 229
Spherical polygon 3 24 81
Spherical polytope 137—138
Spherical simplex 137—143 191—196 284—285 297
Spherical tessellation 64—68 228 291
Spherical tetrahedron xi 139 142 280—284
Spherical triangle 24 109—113 135 138—140
Square {4} 2 121
Star 27 251—258
Star-polygon 93—94
Star-polyhedron 96—111 264—265
Star-polytope 263—287
Staudt, G.K.O. von 1 9
Steiner, Jakob 142
Steinhatis, Hugo 6
Steinitz, Ernst 31
Stella octangula 48—51 56 70 83 96 98
Stellated dodecahedron, great or small 96—98 100
Stellated icosahedron 59
Stellated icosahedron, varieties 32
Stellated triacontahedron, great or small 102—103
Stellating 95—98 204—206
Stiefel, E. 211
Stott, Alicia Boole ix xi 162 163 210 258—259
Stott, Walter 258
Stringham, W.I. 15 136 143 165 209
Studnicka, F.J. 222
Subgroup 42
Summation convention 174
Surface area 22 119 125 293
Surface, algebraic 211 212
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