The Heinz X6 Magic Cube

A 4x4x4 magic cube consists of an array of cells that each hold a number. These numbers are such that each row, column, pillar, and each of the four triagonals sum to the constant.
Imagine a structure such that each cell was actually itself a small cube. If we place a number on each of the six surfaces of each cubelet, it is possible to have 6 magic cubes, one of which is represented by each face of the cubelets. Herein is described a physical model of such a cube.

This model is constructed using sixty-four 3/4" wooden blocks and connected by 1/8" hardwood dowels showing rows, columns, pillars and triagonals. Numbers used are 1 to 384, which is 4³ times 6. This model was completed on July 28, 2002

The six faces of each cubelet are each painted a different color. The 64 cubelet faces of each color form a pantriagonal magic cube with two special features.
It is compact because all 2x2 square arrays within the cube, in all 3 orientations, sum to the constant. This includes wraparound.
It is complete because every pantriagonal contains m/2 complement pairs spaced m/2 apart.
Each of the six cubes is also pantriagonal, because all two and three segment lines parallel to each of the 4 triagonals sums to the correct value!

Unfortunately, the magic constants for these 6 squares are not the same, but vary from 760 to 780. They are:
White = 760, Blue = 764, Red = 768, Pink = 772, Green = 776, Yellow = 780.
Some examples of the 2x2 square arrays are: white, 271 + 133 + 115 + 241 = 760; green, 305 + 95 + 77 + 299 = 776; green (wrap-around), 101 + 281 + 95 + 299 = 776. Compare these with the large copy of picture 1.

Combinations in each cube that equal the magic constant are: rows, columns, pillars = 3 x 4², pantriagonals = 4m², so total lines = 112. 2x2 squares that sum correctly: 4³ x 3 orientations = 192. total combinations for each cube = 304.
The six faces of each of the 64 cubelets sum to 1155. This is because the numbers appearing on opposite faces of each cubelet are members of a complement pair (3 times 385 = 1155).

(Click on a picture for an enlarged view.)

The Six cubes listed

White S = 760
Top                   Top – 1
1 355 217 187   367   37 151 205
373   31 157 199     19 337 235 169
55 301 271 133   313   91   97 259
331   73 115 241    61 295 277 127

Bottom + 1            Bottom
109 247 325   79   283 121   67 289
265 139   49 307   103 253 319   85
163 193 379   25   229 175   13 343
223 181    7 349   145 211 361   43

Blue    S = 764
Top                  Top - 1               Bottom + 1            Bottom
2 356 218 188   368   38 152 206   110 248 326   80   284 122   68 290
374   32 158 200     20 338 236 170   266 140   50 308   104 254 320   86
56 302 272 134   314   92   98 260   164 194 380   26   230 176   14 344
332   74 116 242     62 296 278 128   224 182    8 350   146 212 362   44

Red     S = 768
Top                   Top - 1               Bottom + 1            Bottom
3 357 219 189    369   39 153 207   111 249 327   81   285 123   69 291
375   33 159 201     21 339 237 171   267 141   51 309   105 255 321   87
57 303 273 135   315   93   99 261   165 195 381   27   231 177   15 345
333   75 117 243    63 297 279 129   225 183    9 351   147 213 363   45

Pink     S = 772
Top                   Top - 1               Bottom + 1            Bottom
94 316 262 100    304   58 136 274    178 232 346   16    196 166   28 382
298   64 130 280    76 334 244 118   214 148   46 364   184 226 352   10
40 370 208 154   358    4 190 220   124 286 292   70   250 112   82 328
340   22 172 238     34 376 202 160   256 106   88 322   142 268 310   52

Green S = 776
Top                   Top - 1               Bottom + 1            Bottom
95 317 263 101   305   59 137 275   179 233 347   17   197 167   29 383
299   65 131 281     77 335 245 119   215 149   47 365   185 227 353   11
41 371 209 155    359   5 191 221   125 287 293   71   251 113   83 329
341   23 173 239     35 377 203 161   257 107   89 323   143 269 311   53

Yellow S = 780
Top                   Top - 1               Bottom + 1            Bottom
240 174   24 342   162 204 378   36   324   90 108 258     54 312 270 144
156 210 372   42   222 192   6 360     72 294 288 126   330   84 114 252
282 132   66 300   120 246 336   78   366   48 150 216    12 354 228 186
102 264 318   96   276 138   60 306     18 348 234 180   384   30 168 198