### Pantriagonal 20x20x20 magic cube (Composite 4)

Using a pantriagonal 4x4x4 magic cube and a pantriagonal 5x5x5 magic cube, there are three possibilities to construct a pantriagonal 20x20x20 magic cube.

Take as first grid 125x pantriagonal 4x4x4 magic cube and as second grid 64x pantriagonal 5x5x5 magic cube. See below the grids and result of level 1.

Take 1x number from first grid with 125x pantriagonal 4x4x4 magic cube [level 1]

 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 6 27 54 43 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 51 46 3 30 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 16 17 64 33 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24 57 40 9 24

+64x (number -/- 1) from second grid with 64x pantriagonal 5x5x5 magic cube [level 1]

 10 36 67 98 104 10 36 67 98 104 10 36 67 98 104 10 36 67 98 104 39 70 96 102 8 39 70 96 102 8 39 70 96 102 8 39 70 96 102 8 68 99 105 6 37 68 99 105 6 37 68 99 105 6 37 68 99 105 6 37 97 103 9 40 66 97 103 9 40 66 97 103 9 40 66 97 103 9 40 66 101 7 38 69 100 101 7 38 69 100 101 7 38 69 100 101 7 38 69 100 10 36 67 98 104 10 36 67 98 104 10 36 67 98 104 10 36 67 98 104 39 70 96 102 8 39 70 96 102 8 39 70 96 102 8 39 70 96 102 8 68 99 105 6 37 68 99 105 6 37 68 99 105 6 37 68 99 105 6 37 97 103 9 40 66 97 103 9 40 66 97 103 9 40 66 97 103 9 40 66 101 7 38 69 100 101 7 38 69 100 101 7 38 69 100 101 7 38 69 100 10 36 67 98 104 10 36 67 98 104 10 36 67 98 104 10 36 67 98 104 39 70 96 102 8 39 70 96 102 8 39 70 96 102 8 39 70 96 102 8 68 99 105 6 37 68 99 105 6 37 68 99 105 6 37 68 99 105 6 37 97 103 9 40 66 97 103 9 40 66 97 103 9 40 66 97 103 9 40 66 101 7 38 69 100 101 7 38 69 100 101 7 38 69 100 101 7 38 69 100 10 36 67 98 104 10 36 67 98 104 10 36 67 98 104 10 36 67 98 104 39 70 96 102 8 39 70 96 102 8 39 70 96 102 8 39 70 96 102 8 68 99 105 6 37 68 99 105 6 37 68 99 105 6 37 68 99 105 6 37 97 103 9 40 66 97 103 9 40 66 97 103 9 40 66 97 103 9 40 66 101 7 38 69 100 101 7 38 69 100 101 7 38 69 100 101 7 38 69 100

= 20x20x20 pantriagonal magic cube [level 1]

 582 2267 4278 6251 6598 603 2294 4267 6214 6619 630 2283 4230 6235 6646 619 2246 4251 6262 6635 2483 4462 6083 6494 499 2478 4419 6110 6515 494 2435 4446 6131 6510 451 2462 4467 6126 6467 478 4304 6289 6720 353 2320 4305 6336 6689 336 2321 4352 6305 6672 337 2368 4321 6288 6673 384 2337 6201 6568 521 2520 4217 6184 6537 536 2553 4200 6153 6552 569 2536 4169 6168 6585 552 2505 4184 6406 411 2422 4395 6342 6427 438 2411 4358 6363 6454 427 2374 4379 6390 6443 390 2395 4406 6379 627 2286 4227 6238 6643 622 2243 4254 6259 6638 579 2270 4275 6254 6595 606 2291 4270 6211 6622 2448 4433 6144 6497 464 2449 4480 6113 6480 465 2496 4449 6096 6481 512 2465 4432 6097 6528 481 4345 6312 6665 344 2361 4328 6281 6680 377 2344 4297 6296 6713 360 2313 4312 6329 6696 329 2328 6150 6555 566 2539 4166 6171 6582 555 2502 4187 6198 6571 518 2523 4214 6187 6534 539 2550 4203 6451 430 2371 4382 6387 6446 387 2398 4403 6382 6403 414 2419 4398 6339 6430 435 2414 4355 6366 592 2257 4288 6241 6608 593 2304 4257 6224 6609 640 2273 4240 6225 6656 609 2256 4241 6272 6625 2489 4456 6089 6488 505 2472 4425 6104 6521 488 2441 4440 6137 6504 457 2456 4473 6120 6473 472 4294 6299 6710 363 2310 4315 6326 6699 326 2331 4342 6315 6662 347 2358 4331 6278 6683 374 2347 6195 6574 515 2526 4211 6190 6531 542 2547 4206 6147 6558 563 2542 4163 6174 6579 558 2499 4190 6416 401 2432 4385 6352 6417 448 2401 4368 6353 6464 417 2384 4369 6400 6433 400 2385 4416 6369 633 2280 4233 6232 6649 616 2249 4248 6265 6632 585 2264 4281 6248 6601 600 2297 4264 6217 6616 2438 4443 6134 6507 454 2459 4470 6123 6470 475 2486 4459 6086 6491 502 2475 4422 6107 6518 491 4339 6318 6659 350 2355 4334 6275 6686 371 2350 4291 6302 6707 366 2307 4318 6323 6702 323 2334 6160 6545 576 2529 4176 6161 6592 545 2512 4177 6208 6561 528 2513 4224 6177 6544 529 2560 4193 6457 424 2377 4376 6393 6440 393 2392 4409 6376 6409 408 2425 4392 6345 6424 441 2408 4361 6360

N.B.: Extra magic feature is that each random chosen 4x5 or 5x4 rectangle in the levels and horizontal/vertical through the levels (= 4x5 and 5x4 compact in all three directions) give the magic sum.

See for all levels and 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 4 you use AxAxAx magic cube of order B and BxBxBx magic cube of order A or vice versa to construct a magic cube of order AxB. See on this website the construction of:

20x20x20, pantriagonal (C4).xlsx