### Pantriagonal 7x7x7 magic cube (Composite 1)

Use a specific 7x7 magic square and its row- or column grid to construct a 7x7x7 pantriagonal magic cube.

First we construct the symmetric (but not pan)magic 7x7 square.

Take 1x number from first grid

 4 5 6 0 1 2 3 5 6 0 1 2 3 4 6 0 1 2 3 4 5 0 1 2 3 4 5 6 1 2 3 4 5 6 0 2 3 4 5 6 0 1 3 4 5 6 0 1 2

+7x number from second grid (= first grid turned by a quarter to left)

 3 4 5 6 0 1 2 2 3 4 5 6 0 1 1 2 3 4 5 6 0 0 1 2 3 4 5 6 6 0 1 2 3 4 5 5 6 0 1 2 3 4 4 5 6 0 1 2 3

= 7x7 symmetric magic square

 26 34 42 43 2 10 18 20 28 29 37 45 4 12 14 15 23 31 39 47 6 1 9 17 25 33 41 49 44 3 11 19 27 35 36 38 46 5 13 21 22 30 32 40 48 7 8 16 24

We use the 7x7 magic square and its row- or column grid to construct the middle level (4) of the 7x7x7 pantriagonal magic cube. The grids of the remaining levels are horizontal or vertical shifts of level 4. See below the grids and the result.

Take 1x number from first grid

 175 175 175 175 175 175 175 1 175 44 3 11 19 27 35 36 175 38 46 5 13 21 22 30 175 32 40 48 7 8 16 24 175 26 34 42 43 2 10 18 175 20 28 29 37 45 4 12 175 14 15 23 31 39 47 6 175 1 9 17 25 33 41 49 175 175 175 175 175 175 175 2 175 38 46 5 13 21 22 30 175 32 40 48 7 8 16 24 175 26 34 42 43 2 10 18 175 20 28 29 37 45 4 12 175 14 15 23 31 39 47 6 175 1 9 17 25 33 41 49 175 44 3 11 19 27 35 36 175 175 175 175 175 175 175 3 175 32 40 48 7 8 16 24 175 26 34 42 43 2 10 18 175 20 28 29 37 45 4 12 175 14 15 23 31 39 47 6 175 1 9 17 25 33 41 49 175 44 3 11 19 27 35 36 175 38 46 5 13 21 22 30 175 175 175 175 175 175 175 4 175 26 34 42 43 2 10 18 175 20 28 29 37 45 4 12 175 14 15 23 31 39 47 6 175 1 9 17 25 33 41 49 175 44 3 11 19 27 35 36 175 38 46 5 13 21 22 30 175 32 40 48 7 8 16 24 175 175 175 175 175 175 175 5 175 20 28 29 37 45 4 12 175 14 15 23 31 39 47 6 175 1 9 17 25 33 41 49 175 44 3 11 19 27 35 36 175 38 46 5 13 21 22 30 175 32 40 48 7 8 16 24 175 26 34 42 43 2 10 18 175 175 175 175 175 175 175 6 175 14 15 23 31 39 47 6 175 1 9 17 25 33 41 49 175 44 3 11 19 27 35 36 175 38 46 5 13 21 22 30 175 32 40 48 7 8 16 24 175 26 34 42 43 2 10 18 175 20 28 29 37 45 4 12 175 175 175 175 175 175 175 7 175 1 9 17 25 33 41 49 175 44 3 11 19 27 35 36 175 38 46 5 13 21 22 30 175 32 40 48 7 8 16 24 175 26 34 42 43 2 10 18 175 20 28 29 37 45 4 12 175 14 15 23 31 39 47 6

+49x number from second grid

 21 21 21 21 21 21 21 1 21 0 1 2 3 4 5 6 21 1 2 3 4 5 6 0 21 2 3 4 5 6 0 1 21 3 4 5 6 0 1 2 21 4 5 6 0 1 2 3 21 5 6 0 1 2 3 4 21 6 0 1 2 3 4 5 2 21 6 0 1 2 3 4 5 21 0 1 2 3 4 5 6 21 1 2 3 4 5 6 0 21 2 3 4 5 6 0 1 21 3 4 5 6 0 1 2 21 4 5 6 0 1 2 3 21 5 6 0 1 2 3 4 3 21 5 6 0 1 2 3 4 21 6 0 1 2 3 4 5 21 0 1 2 3 4 5 6 21 1 2 3 4 5 6 0 21 2 3 4 5 6 0 1 21 3 4 5 6 0 1 2 21 4 5 6 0 1 2 3 4 21 4 5 6 0 1 2 3 21 5 6 0 1 2 3 4 21 6 0 1 2 3 4 5 21 0 1 2 3 4 5 6 21 1 2 3 4 5 6 0 21 2 3 4 5 6 0 1 21 3 4 5 6 0 1 2 5 21 3 4 5 6 0 1 2 21 4 5 6 0 1 2 3 21 5 6 0 1 2 3 4 21 6 0 1 2 3 4 5 21 0 1 2 3 4 5 6 21 1 2 3 4 5 6 0 21 2 3 4 5 6 0 1 6 21 2 3 4 5 6 0 1 21 3 4 5 6 0 1 2 21 4 5 6 0 1 2 3 21 5 6 0 1 2 3 4 21 6 0 1 2 3 4 5 21 0 1 2 3 4 5 6 21 1 2 3 4 5 6 0 7 21 1 2 3 4 5 6 0 21 2 3 4 5 6 0 1 21 3 4 5 6 0 1 2 21 4 5 6 0 1 2 3 21 5 6 0 1 2 3 4 21 6 0 1 2 3 4 5 21 0 1 2 3 4 5 6

= 7x7x7 pantriagonal magic cube

 1204 1204 1204 1204 1204 1204 1204 1 1204 44 52 109 166 223 280 330 1204 87 144 152 209 266 316 30 1204 130 187 244 252 302 16 73 1204 173 230 287 337 2 59 116 1204 216 273 323 37 94 102 159 1204 259 309 23 80 137 194 202 1204 295 9 66 123 180 237 294 2 1204 332 46 54 111 168 218 275 1204 32 89 146 154 204 261 318 1204 75 132 189 239 247 304 18 1204 118 175 225 282 339 4 61 1204 161 211 268 325 39 96 104 1204 197 254 311 25 82 139 196 1204 289 297 11 68 125 182 232 3 1204 277 334 48 56 106 163 220 1204 320 34 91 141 149 206 263 1204 20 77 127 184 241 249 306 1204 63 113 170 227 284 341 6 1204 99 156 213 270 327 41 98 1204 191 199 256 313 27 84 134 1204 234 291 299 13 70 120 177 4 1204 222 279 336 43 51 108 165 1204 265 322 29 86 143 151 208 1204 308 15 72 129 186 243 251 1204 1 58 115 172 229 286 343 1204 93 101 158 215 272 329 36 1204 136 193 201 258 315 22 79 1204 179 236 293 301 8 65 122 5 1204 167 224 274 331 45 53 110 1204 210 260 317 31 88 145 153 1204 246 303 17 74 131 188 245 1204 338 3 60 117 174 231 281 1204 38 95 103 160 217 267 324 1204 81 138 195 203 253 310 24 1204 124 181 238 288 296 10 67 6 1204 112 162 219 276 333 47 55 1204 148 205 262 319 33 90 147 1204 240 248 305 19 76 133 183 1204 283 340 5 62 119 169 226 1204 326 40 97 105 155 212 269 1204 26 83 140 190 198 255 312 1204 69 126 176 233 290 298 12 7 1204 50 107 164 221 278 335 49 1204 142 150 207 264 321 35 85 1204 185 242 250 307 21 71 128 1204 228 285 342 7 57 114 171 1204 271 328 42 92 100 157 214 1204 314 28 78 135 192 200 257 1204 14 64 121 178 235 292 300

See for check if all numbers are in the magic cube and addition of the numbers give the right magic sum, the download below.

With method composite 1 you use a magic square to construct a magic cube. See on this website the construction of:

7x7x7, pantriagonal.xls