Pantriagonal 24x24x24 magic cube (Composite 5')

 

Use a 3x3x3 magic cube and it's inverse and a 8x8 most perfect square to construct a pantriagonal 24x24x24 magic cube.

 

The first grid consists of 768x a 3x3x3 magic cube and 768x it's inverse.

 

The second grid consists of a 3x3 'blown up' most perfect 8x8 magic square and it's inverse.

 

The third grid consists of the numbers 0 up to 7.

 

See below the construction of level 1.

 

 

Take 1x number from first grid with 3x3x3 magic cube and it's inverse [level 1]

8

15

19

8

15

19

8

15

19

8

15

19

20

13

9

20

13

9

20

13

9

20

13

9

12

25

5

12

25

5

12

25

5

12

25

5

16

3

23

16

3

23

16

3

23

16

3

23

22

2

18

22

2

18

22

2

18

22

2

18

6

26

10

6

26

10

6

26

10

6

26

10

8

15

19

8

15

19

8

15

19

8

15

19

20

13

9

20

13

9

20

13

9

20

13

9

12

25

5

12

25

5

12

25

5

12

25

5

16

3

23

16

3

23

16

3

23

16

3

23

22

2

18

22

2

18

22

2

18

22

2

18

6

26

10

6

26

10

6

26

10

6

26

10

20

13

9

20

13

9

20

13

9

20

13

9

8

15

19

8

15

19

8

15

19

8

15

19

16

3

23

16

3

23

16

3

23

16

3

23

12

25

5

12

25

5

12

25

5

12

25

5

6

26

10

6

26

10

6

26

10

6

26

10

22

2

18

22

2

18

22

2

18

22

2

18

20

13

9

20

13

9

20

13

9

20

13

9

8

15

19

8

15

19

8

15

19

8

15

19

16

3

23

16

3

23

16

3

23

16

3

23

12

25

5

12

25

5

12

25

5

12

25

5

6

26

10

6

26

10

6

26

10

6

26

10

22

2

18

22

2

18

22

2

18

22

2

18

8

15

19

8

15

19

8

15

19

8

15

19

20

13

9

20

13

9

20

13

9

20

13

9

12

25

5

12

25

5

12

25

5

12

25

5

16

3

23

16

3

23

16

3

23

16

3

23

22

2

18

22

2

18

22

2

18

22

2

18

6

26

10

6

26

10

6

26

10

6

26

10

8

15

19

8

15

19

8

15

19

8

15

19

20

13

9

20

13

9

20

13

9

20

13

9

12

25

5

12

25

5

12

25

5

12

25

5

16

3

23

16

3

23

16

3

23

16

3

23

22

2

18

22

2

18

22

2

18

22

2

18

6

26

10

6

26

10

6

26

10

6

26

10

20

13

9

20

13

9

20

13

9

20

13

9

8

15

19

8

15

19

8

15

19

8

15

19

16

3

23

16

3

23

16

3

23

16

3

23

12

25

5

12

25

5

12

25

5

12

25

5

6

26

10

6

26

10

6

26

10

6

26

10

22

2

18

22

2

18

22

2

18

22

2

18

20

13

9

20

13

9

20

13

9

20

13

9

8

15

19

8

15

19

8

15

19

8

15

19

16

3

23

16

3

23

16

3

23

16

3

23

12

25

5

12

25

5

12

25

5

12

25

5

6

26

10

6

26

10

6

26

10

6

26

10

22

2

18

22

2

18

22

2

18

22

2

18

 

 

+27x number from second grid with 3x3x3 'blown up' most perfect 8x8 magic square [level 1]

1

1

1

60

60

60

22

22

22

47

47

47

2

2

2

59

59

59

21

21

21

48

48

48

1

1

1

60

60

60

22

22

22

47

47

47

2

2

2

59

59

59

21

21

21

48

48

48

1

1

1

60

60

60

22

22

22

47

47

47

2

2

2

59

59

59

21

21

21

48

48

48

56

56

56

13

13

13

35

35

35

26

26

26

55

55

55

14

14

14

36

36

36

25

25

25

56

56

56

13

13

13

35

35

35

26

26

26

55

55

55

14

14

14

36

36

36

25

25

25

56

56

56

13

13

13

35

35

35

26

26

26

55

55

55

14

14

14

36

36

36

25

25

25

43

43

43

18

18

18

64

64

64

5

5

5

44

44

44

17

17

17

63

63

63

6

6

6

43

43

43

18

18

18

64

64

64

5

5

5

44

44

44

17

17

17

63

63

63

6

6

6

43

43

43

18

18

18

64

64

64

5

5

5

44

44

44

17

17

17

63

63

63

6

6

6

30

30

30

39

39

39

9

9

9

52

52

52

29

29

29

40

40

40

10

10

10

51

51

51

30

30

30

39

39

39

9

9

9

52

52

52

29

29

29

40

40

40

10

10

10

51

51

51

30

30

30

39

39

39

9

9

9

52

52

52

29

29

29

40

40

40

10

10

10

51

51

51

3

3

3

58

58

58

24

24

24

45

45

45

4

4

4

57

57

57

23

23

23

46

46

46

3

3

3

58

58

58

24

24

24

45

45

45

4

4

4

57

57

57

23

23

23

46

46

46

3

3

3

58

58

58

24

24

24

45

45

45

4

4

4

57

57

57

23

23

23

46

46

46

54

54

54

15

15

15

33

33

33

28

28

28

53

53

53

16

16

16

34

34

34

27

27

27

54

54

54

15

15

15

33

33

33

28

28

28

53

53

53

16

16

16

34

34

34

27

27

27

54

54

54

15

15

15

33

33

33

28

28

28

53

53

53

16

16

16

34

34

34

27

27

27

41

41

41

20

20

20

62

62

62

7

7

7

42

42

42

19

19

19

61

61

61

8

8

8

41

41

41

20

20

20

62

62

62

7

7

7

42

42

42

19

19

19

61

61

61

8

8

8

41

41

41

20

20

20

62

62

62

7

7

7

42

42

42

19

19

19

61

61

61

8

8

8

32

32

32

37

37

37

11

11

11

50

50

50

31

31

31

38

38

38

12

12

12

49

49

49

32

32

32

37

37

37

11

11

11

50

50

50

31

31

31

38

38

38

12

12

12

49

49

49

32

32

32

37

37

37

11

11

11

50

50

50

31

31

31

38

38

38

12

12

12

49

49

49

 

 

+27x64x number from third grid with numbers 0 up to 7 [level 1]

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

7

7

7

0

0

0

 

 

= pantriagonal 24x24x24 magic cube [level 1]

8

15

19

13697

13704

13708

575

582

586

13346

13353

13357

47

40

36

13682

13675

13671

560

553

549

13385

13378

13374

12

25

5

13701

13714

13694

579

592

572

13350

13363

13343

43

30

50

13678

13665

13685

556

543

563

13381

13368

13388

22

2

18

13711

13691

13707

589

569

585

13360

13340

13356

33

53

37

13668

13688

13672

546

566

550

13371

13391

13375

13589

13596

13600

332

339

343

13022

13029

13033

683

690

694

13574

13567

13563

371

364

360

13061

13054

13050

668

661

657

13593

13606

13586

336

349

329

13026

13039

13019

687

700

680

13570

13557

13577

367

354

374

13057

13044

13064

664

651

671

13603

13583

13599

346

326

342

13036

13016

13032

697

677

693

13560

13580

13564

357

377

361

13047

13067

13051

654

674

658

1154

1147

1143

12575

12568

12564

1721

1714

1710

12224

12217

12213

1169

1176

1180

12536

12543

12547

1682

1689

1693

12239

12246

12250

1150

1137

1157

12571

12558

12578

1717

1704

1724

12220

12207

12227

1173

1186

1166

12540

12553

12533

1686

1699

1679

12243

12256

12236

1140

1160

1144

12561

12581

12565

1707

1727

1711

12210

12230

12214

1183

1163

1179

12550

12530

12546

1696

1676

1692

12253

12233

12249

12899

12892

12888

1046

1039

1035

12332

12325

12321

1397

1390

1386

12860

12867

12871

1061

1068

1072

12347

12354

12358

1358

1365

1369

12895

12882

12902

1042

1029

1049

12328

12315

12335

1393

1380

1400

12864

12877

12857

1065

1078

1058

12351

12364

12344

1362

1375

1355

12885

12905

12889

1032

1052

1036

12318

12338

12322

1383

1403

1387

12874

12854

12870

1075

1055

1071

12361

12341

12357

1372

1352

1368

62

69

73

13643

13650

13654

629

636

640

13292

13299

13303

101

94

90

13628

13621

13617

614

607

603

13331

13324

13320

66

79

59

13647

13660

13640

633

646

626

13296

13309

13289

97

84

104

13624

13611

13631

610

597

617

13327

13314

13334

76

56

72

13657

13637

13653

643

623

639

13306

13286

13302

87

107

91

13614

13634

13618

600

620

604

13317

13337

13321

13535

13542

13546

386

393

397

12968

12975

12979

737

744

748

13520

13513

13509

425

418

414

13007

13000

12996

722

715

711

13539

13552

13532

390

403

383

12972

12985

12965

741

754

734

13516

13503

13523

421

408

428

13003

12990

13010

718

705

725

13549

13529

13545

400

380

396

12982

12962

12978

751

731

747

13506

13526

13510

411

431

415

12993

13013

12997

708

728

712

1100

1093

1089

12629

12622

12618

1667

1660

1656

12278

12271

12267

1115

1122

1126

12590

12597

12601

1628

1635

1639

12293

12300

12304

1096

1083

1103

12625

12612

12632

1663

1650

1670

12274

12261

12281

1119

1132

1112

12594

12607

12587

1632

1645

1625

12297

12310

12290

1086

1106

1090

12615

12635

12619

1653

1673

1657

12264

12284

12268

1129

1109

1125

12604

12584

12600

1642

1622

1638

12307

12287

12303

12953

12946

12942

992

985

981

12386

12379

12375

1343

1336

1332

12914

12921

12925

1007

1014

1018

12401

12408

12412

1304

1311

1315

12949

12936

12956

988

975

995

12382

12369

12389

1339

1326

1346

12918

12931

12911

1011

1024

1004

12405

12418

12398

1308

1321

1301

12939

12959

12943

978

998

982

12372

12392

12376

1329

1349

1333

12928

12908

12924

1021

1001

1017

12415

12395

12411

1318

1298

1314

 

 

N.B.: In the pantriagonal magic cube 1/2 rows/columns/pillars give 1/2 of the magic sum.

 

See in the download below the construction of all levels, check if all formulas give the valid magic sum and check if all numbers are in the magic cube.

 

With method composite 5' you use a 3x3x3 magic cube and its inverse and a 4x4 panmagic square or a most perfect 8x8 magic square to construct a pantriagonal magic cube. See on this website the construction of:

12x12x12 and 24x24x24

 

Download
24x24x24, pantriagonal (C5').xlsx
Microsoft Excel werkblad 1.1 MB