Description Usage Arguments Details Author(s) Examples
Returns magic hypercubes of order 4n and any dimension.
1 | magichypercube.4n(m, d = 3)
|
m |
Magic hypercube produced of order n=4m |
d |
Dimensionality of cube |
Uses a rather kludgy (but vectorized) method. I am not 100% sure that the method does in fact produce magic squares for all orders and dimensions.
Robin K. S. Hankin
1 2 | magichypercube.4n(1,d=4)
magichypercube.4n(2,d=3)
|
Loading required package: abind
, , 1, 1
[,1] [,2] [,3] [,4]
[1,] 1 252 248 13
[2,] 255 6 10 243
[3,] 254 7 11 242
[4,] 4 249 245 16
, , 2, 1
[,1] [,2] [,3] [,4]
[1,] 240 21 25 228
[2,] 18 235 231 30
[3,] 19 234 230 31
[4,] 237 24 28 225
, , 3, 1
[,1] [,2] [,3] [,4]
[1,] 224 37 41 212
[2,] 34 219 215 46
[3,] 35 218 214 47
[4,] 221 40 44 209
, , 4, 1
[,1] [,2] [,3] [,4]
[1,] 49 204 200 61
[2,] 207 54 58 195
[3,] 206 55 59 194
[4,] 52 201 197 64
, , 1, 2
[,1] [,2] [,3] [,4]
[1,] 192 69 73 180
[2,] 66 187 183 78
[3,] 67 186 182 79
[4,] 189 72 76 177
, , 2, 2
[,1] [,2] [,3] [,4]
[1,] 81 172 168 93
[2,] 175 86 90 163
[3,] 174 87 91 162
[4,] 84 169 165 96
, , 3, 2
[,1] [,2] [,3] [,4]
[1,] 97 156 152 109
[2,] 159 102 106 147
[3,] 158 103 107 146
[4,] 100 153 149 112
, , 4, 2
[,1] [,2] [,3] [,4]
[1,] 144 117 121 132
[2,] 114 139 135 126
[3,] 115 138 134 127
[4,] 141 120 124 129
, , 1, 3
[,1] [,2] [,3] [,4]
[1,] 128 133 137 116
[2,] 130 123 119 142
[3,] 131 122 118 143
[4,] 125 136 140 113
, , 2, 3
[,1] [,2] [,3] [,4]
[1,] 145 108 104 157
[2,] 111 150 154 99
[3,] 110 151 155 98
[4,] 148 105 101 160
, , 3, 3
[,1] [,2] [,3] [,4]
[1,] 161 92 88 173
[2,] 95 166 170 83
[3,] 94 167 171 82
[4,] 164 89 85 176
, , 4, 3
[,1] [,2] [,3] [,4]
[1,] 80 181 185 68
[2,] 178 75 71 190
[3,] 179 74 70 191
[4,] 77 184 188 65
, , 1, 4
[,1] [,2] [,3] [,4]
[1,] 193 60 56 205
[2,] 63 198 202 51
[3,] 62 199 203 50
[4,] 196 57 53 208
, , 2, 4
[,1] [,2] [,3] [,4]
[1,] 48 213 217 36
[2,] 210 43 39 222
[3,] 211 42 38 223
[4,] 45 216 220 33
, , 3, 4
[,1] [,2] [,3] [,4]
[1,] 32 229 233 20
[2,] 226 27 23 238
[3,] 227 26 22 239
[4,] 29 232 236 17
, , 4, 4
[,1] [,2] [,3] [,4]
[1,] 241 12 8 253
[2,] 15 246 250 3
[3,] 14 247 251 2
[4,] 244 9 5 256
, , 1
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 512 9 17 488 480 41 49 456
[2,] 2 503 495 26 34 471 463 58
[3,] 3 502 494 27 35 470 462 59
[4,] 509 12 20 485 477 44 52 453
[5,] 508 13 21 484 476 45 53 452
[6,] 6 499 491 30 38 467 459 62
[7,] 7 498 490 31 39 466 458 63
[8,] 505 16 24 481 473 48 56 449
, , 2
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 65 440 432 89 97 408 400 121
[2,] 447 74 82 423 415 106 114 391
[3,] 446 75 83 422 414 107 115 390
[4,] 68 437 429 92 100 405 397 124
[5,] 69 436 428 93 101 404 396 125
[6,] 443 78 86 419 411 110 118 387
[7,] 442 79 87 418 410 111 119 386
[8,] 72 433 425 96 104 401 393 128
, , 3
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 129 376 368 153 161 344 336 185
[2,] 383 138 146 359 351 170 178 327
[3,] 382 139 147 358 350 171 179 326
[4,] 132 373 365 156 164 341 333 188
[5,] 133 372 364 157 165 340 332 189
[6,] 379 142 150 355 347 174 182 323
[7,] 378 143 151 354 346 175 183 322
[8,] 136 369 361 160 168 337 329 192
, , 4
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 320 201 209 296 288 233 241 264
[2,] 194 311 303 218 226 279 271 250
[3,] 195 310 302 219 227 278 270 251
[4,] 317 204 212 293 285 236 244 261
[5,] 316 205 213 292 284 237 245 260
[6,] 198 307 299 222 230 275 267 254
[7,] 199 306 298 223 231 274 266 255
[8,] 313 208 216 289 281 240 248 257
, , 5
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 256 265 273 232 224 297 305 200
[2,] 258 247 239 282 290 215 207 314
[3,] 259 246 238 283 291 214 206 315
[4,] 253 268 276 229 221 300 308 197
[5,] 252 269 277 228 220 301 309 196
[6,] 262 243 235 286 294 211 203 318
[7,] 263 242 234 287 295 210 202 319
[8,] 249 272 280 225 217 304 312 193
, , 6
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 321 184 176 345 353 152 144 377
[2,] 191 330 338 167 159 362 370 135
[3,] 190 331 339 166 158 363 371 134
[4,] 324 181 173 348 356 149 141 380
[5,] 325 180 172 349 357 148 140 381
[6,] 187 334 342 163 155 366 374 131
[7,] 186 335 343 162 154 367 375 130
[8,] 328 177 169 352 360 145 137 384
, , 7
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 385 120 112 409 417 88 80 441
[2,] 127 394 402 103 95 426 434 71
[3,] 126 395 403 102 94 427 435 70
[4,] 388 117 109 412 420 85 77 444
[5,] 389 116 108 413 421 84 76 445
[6,] 123 398 406 99 91 430 438 67
[7,] 122 399 407 98 90 431 439 66
[8,] 392 113 105 416 424 81 73 448
, , 8
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 64 457 465 40 32 489 497 8
[2,] 450 55 47 474 482 23 15 506
[3,] 451 54 46 475 483 22 14 507
[4,] 61 460 468 37 29 492 500 5
[5,] 60 461 469 36 28 493 501 4
[6,] 454 51 43 478 486 19 11 510
[7,] 455 50 42 479 487 18 10 511
[8,] 57 464 472 33 25 496 504 1
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