Index 2D system, 127, 221 3D consistency, 128, 151, 158, 221, 224, 225, 261, 314, 316 3D system, 34, 44, 63, 67, 89, 272 4D consistency, 36, 37, 45, 63, 70, 91, 272 5-point sphere, 146 A-net, 66, 82, 119, 130 convergence, 199 in a quadric, 121 A-surface, 11, 66 associated family, 180, 211 associated point, 99, 121 asymptotic line parametrized surface, 11, 66 B¨ acklund transformation, xvi, xviii, 21, 133, 142, 179, 209, 211, 214, 224, 318 convergence, 205 Bianchi permutability, xviii, 212, 215 Bianchi quadrilateral, 1 bilinear cube equation, 277 bilinear Hirota equation, 285 bilinear octahedron equation, 285 biquadratic, 240 nondegenerate, 241 Brianchon theorem, 165, 366 Calapso transformation, 182 Carnot theorem, 364 Cauchy problem, 228 Cauchy-Riemann equation, 291, 292, 294 integrable, 297 Chebyshev net, 20 Chebyshev quadrilateral, 130, 145, 179, 282 Christoffel dual net, 7, 23, 27, 49, 58, 156, 168, 175, 176 circle pattern, 311 integrable, 317 isoradial, 317 circular net, 88, 117, 145, 177 convergence, 202, 203 Clifford algebra, 349 Clifford configuration, 147 Clifford group, 349 Clifford’s chain of theorems, 121 Combescure transformation, 5, 47, 170 commuting flows, xvi, xviii, 209 conical net, 103, 117, 177 conjugate harmonic function, 291, 292 conjugate net, 2 contact element, 17, 106, 118, 177, 336, 354 continuous limit, xviii, 42, 60, 160 cross-ratio, 24, 77, 121, 147, 173, 357 cross-ratio equation, 222, 314 in associative algebra, 236 curvature line parametrized surface, 16, 88, 115 Darboux system, 4, 42, 273 Darboux transformation, xvi, xviii, 23, 26, 151 Desargues theorem, 149, 361 discrete wa−1, 320 discrete za, 320 discrete Amsler surface, 180 discrete asymptotic net, 66 discrete BKP equation, 81, 277 discrete Calapso equation, 237 discrete conjugate net, 32 discrete differential geometry, xiii, xviii 401

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