6-D MASTER BASE LINES

Determination of integer at position 55, 20, 3, 34, 16, 45
decimalmaster base line in binary
5541000000000000000000000000000000101000
2068719473919111111111111111111111111010011111110
312287000000000000000000000010111111111110
3416252928000000000000111101111111111111111111
16268435455000000001111111111111111111111111110
4554760833024110010111111111111111111111111111111
bitwise exclusive OR combination or (mod 2)
14210835670001101001111000010000010010011010110

As discussed in Basic Construction the master base lines can be used to generate any of the numbers in the magic figure. The master base lines for the 6-D figure consist of the numbers that start at zero and follow each of the hypercubes six axes. Each consists of 64 numbers starting with zero. They can be obtained from the Sample Nasik 6-D Magic Hypercube table by creating a separate 36 x 64 spreadsheet for each of the columns of that table. The 64 binary bits of each code in the table's column are entered in the rows. The 64 numbers of the master base line for that dimension are the numerical equivalents of the 36 bits in each column of the new table. The master base lines in the table below were created in this way from the alphanumeric codes on the n-Dimensions page.

From the master base lines, it is easy to get a number at any location within the hypercube. For instance the number at the intersection of the 55th row, 20th column, 3rd pillar, 34th file, 16th 5-D, and 45th 6-D will be the six way exclusive OR combination of the 36 bits of the binary equivalents of 41, 68719473919, 12287, 16252928, 268435455, and 54760833024. The calculation is shown in the table above. First the six numbers are converted to 36-bit numbers. Then the six bits in each column are combined using the exclusive OR function or by summing the numbers (mod 2). This gives the 36-bit number at the bottom that is converted back to its decimal equivalent, 14210835670. This type of binary manipulation is easily accomplished by computer.

Master Base Lines of 6-D Hypercube
Position #rowcolumnpillarfilefifthsixth
1000000
2687194766731274096262144167772161073741824
326871947276812287524288335544322147483648
4687194766756871947289516383786432503316483221225472
54256687192309761310719671088644294967296
668719476677383687192350721572863838860805368709120
76687194730246871924326318350071006632966442450944
868719476679687194731516871924735920971511174405127516192768
9851232768687047966721509949438589934592
106871947668163936864687050588161677721599663676416
111068719473280450556870532096018454937510737418240
126871947668368719473407491516870558310420132659111811160064
1312768687192637446870610739121810380712884901888
1468719476685895687192678406870636953523488102313958643712
151468719473536687192760316870663167925165823915032385536
166871947668768719473663687192801276870689382326843545516106127360
171610246553641943046791417036818253611007
186871947668911516963244564486793094758419327352831
1918687194737927782347185926794772480020401094655
2068719476691687194739198191949807366796450201621474836479
212012806871929651255050236798127923222548578303
226871947669314076871930060857671676799805644823622320127
2322687194740486871930879960293116801483366424696061951
2468719476695687194741756871931289562914556803161088025769803775
2524153698304687089909766806516531126843545599
26687194766971663102400687092531206808194252727917287423
272668719474304110591687095152646809871974328991029247
286871947669968719474431114687687097774086811549695930064771071
2928179268719329280687103016956813227417531138512895
3068719476701191968719333376687105638396814905139132212254719
31306871947456068719341567687108259836816582860733285996543
32687194767036871947468768719345663687110881276818260582334359738367
3363403225804816515072105696460867645734912
3468719476734403125395216252928104018739266571993088
35616871947654425395115990784102341017665498251264
36687194767326871947654324985515728640100663296064424509440
37593776687194562561572863998985574463350767616
38687194767303775687194521601546649597307852862277025792
395768719476288687194521591520435195630131261203283968
406871947672868719476287687194480631494220793952409660129542144
415535202252806871711744093952409559055800320
426871947672635192211846871685529692274687957982058496
4353687194760322211836871659315290596966356908316672
4468719476724687194760312170876871633100888919244755834574848
45513264687194234886871633100787241523154760833024
46687194767223263687194193926871606886385563801553687091200
474968719475776687194193916871580671983886079952613349376
486871947672068719475775687194152956871554457582208358351539607552
49473008192512123207686843426406451539607551
50687194767183007188416120586246841748684850465865727
514568719475520188415117964806840070963249392123903
526871947671668719475519184319115343366838393241648318382079
5343275268719390720115343356836715520047244640255
5468719476714275168719386624112721916835037798446170898431
55416871947526468719386623110100476833360076845097156607
56687194767126871947526368719382527107479036831682355244023414783
57392496159744687129231366831682355142949672959
58687194767102495155648687126609926830004633541875931135
593768719475008155647687123988486828326911940802189311
606871947670868719475007151551687121367046826649190339728447487
6135224068719357952687121367036824971468738654705663
6268719476706223968719353856687118745596823293747137580963839
63336871947475268719353855687116124156821616025536507222015
64687194767046871947475168719349759687113502716819938303935433480191