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Algorithm to make diagonal magic cubes (example for order 10)

   The following figures are concrete expressions of G8(v, z), bijk, cijk, dijk, eijk, and aijk for m = 10. The cube aijk is an order-10 diagonal magic cube generated by bijk, cijk, dijk, and eijk. Definitions of them are here.
   Compare with the case of an associated pantriagonal magic cube.

G8(v, z)
(v,z)01234
001377
110736
223265
332624
445153
554512
667041
776400

bijk
bijk (k = 0)
0137742623
1377024263
3770123426
7701362342
7013726234
2445140771
1255506614
5124477140
4512571406
5551214066
bijk (k = 1)
7701362342
7013726234
0137742632
1377034262
3770123426
5125566140
4512471407
5451214067
2555140661
1244507714
bijk (k = 2)
1377034262
3770123426
7701362342
7013726324
0137742623
4451214077
2545140671
1255506614
5124477140
5512561406

bijk (k = 3)
7013726234
0137742623
1377034262
3770123426
7701363242
1254506714
5125566140
4512471407
5551214066
2445140771
bijk (k = 4)
3770132426
7701362342
7013726234
0137742623
1377034262
5512561406
4451214077
2555140661
1244507714
5125467140
bijk (k = 5)
7361023562
3610723256
6107362325
1073656232
0736125623
4153470047
5515300466
3441504770
5355146600
1534576004

bijk (k = 6)
6107362325
1073656232
0736125623
7361032562
3610722356
5345147600
1534477004
5153560046
4415300477
3551504660
bijk (k = 7)
0736125623
7361032562
3610723256
6107362235
1073656232
5515300466
3451504760
5344147700
1535566004
4153470047
bijk (k = 8)
3610723256
6107362325
1073656223
0736125623
7361032562
1534477004
5153560046
4515300476
3441504770
5355146600

bijk (k = 9)
1073656232
0736135622
7361032562
3610723256
6107362325
3551504660
5344147700
1535566004
5153460047
4415300477
cijk
cijk (k = 0)
0123443210
2340110432
4012332104
1234004321
3401221043
3401221043
1234004321
4012332104
2340110432
0123443210
cijk (k = 1)
1234004321
3401221043
0123443210
2340110432
4012332104
4012332104
2340110432
0123443210
3401221043
1234004321
cijk (k = 2)
2340110432
4012332104
1234004321
3401221043
0123443210
0123443210
3401221043
1234004321
4012332104
2340110432

cijk (k = 3)
3401221043
0123443210
2340110432
4012332104
1234004321
1234004321
4012332104
2340110432
0123443210
3401221043
cijk (k = 4)
4012332104
1234004321
3401221043
0123443210
2340110432
2340110432
0123443210
3401221043
1234004321
4012332104
cijk (k = 5)
4012332104
1234004321
3401221043
0123443210
2340110432
2340110432
0123443210
3401221043
1234004321
4012332104

cijk (k = 6)
3401221043
0123443210
2340110432
4012332104
1234004321
1234004321
4012332104
2340110432
0123443210
3401221043
cijk (k = 7)
2340110432
4012332104
1234004321
3401221043
0123443210
0123443210
3401221043
1234004321
4012332104
2340110432
cijk (k = 8)
1234004321
3401221043
0123443210
2340110432
4012332104
4012332104
2340110432
0123443210
3401221043
1234004321

cijk (k = 9)
0123443210
2340110432
4012332104
1234004321
3401221043
3401221043
1234004321
4012332104
2340110432
0123443210
dijk
dijk (k = 0)
0241331420
1302442031
2413003142
3024114203
4130220314
4130220314
3024114203
2413003142
1302442031
0241331420
dijk (k = 1)
1302442031
2413003142
3024114203
4130220314
0241331420
0241331420
4130220314
3024114203
2413003142
1302442031
dijk (k = 2)
2413003142
3024114203
4130220314
0241331420
1302442031
1302442031
0241331420
4130220314
3024114203
2413003142

dijk (k = 3)
3024114203
4130220314
0241331420
1302442031
2413003142
2413003142
1302442031
0241331420
4130220314
3024114203
dijk (k = 4)
4130220314
0241331420
1302442031
2413003142
3024114203
3024114203
2413003142
1302442031
0241331420
4130220314
dijk (k = 5)
4130220314
0241331420
1302442031
2413003142
3024114203
3024114203
2413003142
1302442031
0241331420
4130220314

dijk (k = 6)
3024114203
4130220314
0241331420
1302442031
2413003142
2413003142
1302442031
0241331420
4130220314
3024114203
dijk (k = 7)
2413003142
3024114203
4130220314
0241331420
1302442031
1302442031
0241331420
4130220314
3024114203
2413003142
dijk (k = 8)
1302442031
2413003142
3024114203
4130220314
0241331420
0241331420
4130220314
3024114203
2413003142
1302442031

dijk (k = 9)
0241331420
1302442031
2413003142
3024114203
4130220314
4130220314
3024114203
2413003142
1302442031
0241331420
eijk
eijk (k = 0)
0123443210
1234004321
2340110432
3401221043
4012332104
4012332104
3401221043
2340110432
1234004321
0123443210
eijk (k = 1)
2340110432
3401221043
4012332104
0123443210
1234004321
1234004321
0123443210
4012332104
3401221043
2340110432
eijk (k = 2)
4012332104
0123443210
1234004321
2340110432
3401221043
3401221043
2340110432
1234004321
0123443210
4012332104

eijk (k = 3)
1234004321
2340110432
3401221043
4012332104
0123443210
0123443210
4012332104
3401221043
2340110432
1234004321
eijk (k = 4)
3401221043
4012332104
0123443210
1234004321
2340110432
2340110432
1234004321
0123443210
4012332104
3401221043
eijk (k = 5)
3401221043
4012332104
0123443210
1234004321
2340110432
2340110432
1234004321
0123443210
4012332104
3401221043

eijk (k = 6)
1234004321
2340110432
3401221043
4012332104
0123443210
0123443210
4012332104
3401221043
2340110432
1234004321
eijk (k = 7)
4012332104
0123443210
1234004321
2340110432
3401221043
3401221043
2340110432
1234004321
0123443210
4012332104
eijk (k = 8)
2340110432
3401221043
4012332104
0123443210
1234004321
1234004321
0123443210
4012332104
3401221043
2340110432

eijk (k = 9)
0123443210
1234004321
2340110432
3401221043
4012332104
4012332104
3401221043
2340110432
1234004321
0123443210
an order-10 diagonal magic cube aijk
Plane No.1 (aijk, k = 0)
1162448959995620334823287376
18246897989046296515354843432
48889991066202327441535274863
91993086247383758372461555294
975106142403939314778267481600
35060651765318956428892981225
1693057117476338872836180544
738149285566577952941160524113
55771822926567192114060493807
62666269820937024558473787751
Plane No.2 (aijk, k = 1)
90894480236397772361455569283
964125131417928303792256500589
20151437973984609348812401270
19645799387940415504368832321
47788892460216341435549263852
727138299685716841810174513102
57170724325454091512961882946
64552668722335923459862776895
33975063166717855342756875214
15831958061164722986955194533
Plane No.3 (aijk, k = 2)
19047198289329404518357846315
49187791374210335449538252866
92293394230386761355469558297
953114150406942317781400364578
9170426962998623337801295384
50954567621237324858751920884
32873952565619256731775989203
17230871973063611855844183547
741127288574585960949163502116
69072123226865477914360796815

Plane No.4 (aijk, k = 3)
967103139425931306800264478592
23159445951987612326820284398
17946599688243418507371840304
48589190263224349438527266860
91194783244380755494333572286
1613227086196305869958197536
735141277688724849813152516110
55471524625754391813262190929
64865969520136223757670784773
34260351467518155650889978217
Plane No.5 (aijk, k = 4)
49988591652213463302541260874
90593697233394769358472561280
956117128414950325789253492581
12173434970976601345809298387
19345499089632407521365829318
69370424027165778214661579818
51254868422035122659559923887
33174262866420057539753867206
15531159760864419983972186530
749135291677588838927166510124
Plane No.6 (aijk, k = 5)
99938579117788338427666760374
405811222108894269483347686780
8312423914450825289378367706
13748934470851726845309423262
68954490771157282646865329443
56820474039653290721115579943
63767318472047610195559798762
4566175031647007553987899281
6554367227331445198588476130
2496354165527139638024110624

Plane No.7 (aijk, k = 6)
84222814925431806300389353717
14834945451862737826320409273
54965496757168293632871340429
98539177718899474313652766360
411822208119880255369458697786
6614475837441305059948337236
2356414025635999749382716610
6792157463826687937121590804
52353419570148711276570909898
4677286391756815655076485392
Plane No.8 (aijk, k = 7)
65971482768154279643857346440
99137778819985460324663752366
422808219105886261480344683797
82823925906442817281275489703
13445926462873748837301420259
63467017671249812387551795759
4536146501566926753190086478
6724335946051365119809695847
241627413699710835824382616
56522173239352990418107596940
Plane No.9 (aijk, k = 8)
408819205111897272486330694783
8392506917428803292381375714
14526937473859734848312276395
71957493754165290629868332446
97738879918591466310674763352
2276384245605919669354913602
6962077433796657904118582821
52065118772348410998562901770
46462550616767853542881100089
6584447057361475228618306933

Plane No.10 (aijk, k = 9)
12637948459870745834323412251
57968479765171421640854343307
98839978519177452316660774363
419805211122883258497336680794
85023117903439814278392356725
47573164215368964528767856100
6694305866221335089979615544
2386494106917028278163524613
68221872939054679615104593932
50153719870949512084573912876


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This page was last updated on August 8, 2016.
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