# 6-D MASTER BASE LINES

 decimal master base line in binary 55 41 000000000000000000000000000000101000 20 68719473919 111111111111111111111111010011111110 3 12287 000000000000000000000010111111111110 34 16252928 000000000000111101111111111111111111 16 268435455 000000001111111111111111111111111110 45 54760833024 110010111111111111111111111111111111 bitwise exclusive OR combination or (mod 2) 14210835670 001101001111000010000010010011010110

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.

 Position # row column pillar file fifth sixth 1 0 0 0 0 0 0 2 68719476673 127 4096 262144 16777216 1073741824 3 2 68719472768 12287 524288 33554432 2147483648 4 68719476675 68719472895 16383 786432 50331648 3221225472 5 4 256 68719230976 1310719 67108864 4294967296 6 68719476677 383 68719235072 1572863 83886080 5368709120 7 6 68719473024 68719243263 1835007 100663296 6442450944 8 68719476679 68719473151 68719247359 2097151 117440512 7516192768 9 8 512 32768 68704796672 150994943 8589934592 10 68719476681 639 36864 68705058816 167772159 9663676416 11 10 68719473280 45055 68705320960 184549375 10737418240 12 68719476683 68719473407 49151 68705583104 201326591 11811160064 13 12 768 68719263744 68706107391 218103807 12884901888 14 68719476685 895 68719267840 68706369535 234881023 13958643712 15 14 68719473536 68719276031 68706631679 251658239 15032385536 16 68719476687 68719473663 68719280127 68706893823 268435455 16106127360 17 16 1024 65536 4194304 67914170368 18253611007 18 68719476689 1151 69632 4456448 67930947584 19327352831 19 18 68719473792 77823 4718592 67947724800 20401094655 20 68719476691 68719473919 81919 4980736 67964502016 21474836479 21 20 1280 68719296512 5505023 67981279232 22548578303 22 68719476693 1407 68719300608 5767167 67998056448 23622320127 23 22 68719474048 68719308799 6029311 68014833664 24696061951 24 68719476695 68719474175 68719312895 6291455 68031610880 25769803775 25 24 1536 98304 68708990976 68065165311 26843545599 26 68719476697 1663 102400 68709253120 68081942527 27917287423 27 26 68719474304 110591 68709515264 68098719743 28991029247 28 68719476699 68719474431 114687 68709777408 68115496959 30064771071 29 28 1792 68719329280 68710301695 68132274175 31138512895 30 68719476701 1919 68719333376 68710563839 68149051391 32212254719 31 30 68719474560 68719341567 68710825983 68165828607 33285996543 32 68719476703 68719474687 68719345663 68711088127 68182605823 34359738367 33 63 4032 258048 16515072 1056964608 67645734912 34 68719476734 4031 253952 16252928 1040187392 66571993088 35 61 68719476544 253951 15990784 1023410176 65498251264 36 68719476732 68719476543 249855 15728640 1006632960 64424509440 37 59 3776 68719456256 15728639 989855744 63350767616 38 68719476730 3775 68719452160 15466495 973078528 62277025792 39 57 68719476288 68719452159 15204351 956301312 61203283968 40 68719476728 68719476287 68719448063 14942207 939524096 60129542144 41 55 3520 225280 68717117440 939524095 59055800320 42 68719476726 3519 221184 68716855296 922746879 57982058496 43 53 68719476032 221183 68716593152 905969663 56908316672 44 68719476724 68719476031 217087 68716331008 889192447 55834574848 45 51 3264 68719423488 68716331007 872415231 54760833024 46 68719476722 3263 68719419392 68716068863 855638015 53687091200 47 49 68719475776 68719419391 68715806719 838860799 52613349376 48 68719476720 68719475775 68719415295 68715544575 822083583 51539607552 49 47 3008 192512 12320768 68434264064 51539607551 50 68719476718 3007 188416 12058624 68417486848 50465865727 51 45 68719475520 188415 11796480 68400709632 49392123903 52 68719476716 68719475519 184319 11534336 68383932416 48318382079 53 43 2752 68719390720 11534335 68367155200 47244640255 54 68719476714 2751 68719386624 11272191 68350377984 46170898431 55 41 68719475264 68719386623 11010047 68333600768 45097156607 56 68719476712 68719475263 68719382527 10747903 68316823552 44023414783 57 39 2496 159744 68712923136 68316823551 42949672959 58 68719476710 2495 155648 68712660992 68300046335 41875931135 59 37 68719475008 155647 68712398848 68283269119 40802189311 60 68719476708 68719475007 151551 68712136704 68266491903 39728447487 61 35 2240 68719357952 68712136703 68249714687 38654705663 62 68719476706 2239 68719353856 68711874559 68232937471 37580963839 63 33 68719474752 68719353855 68711612415 68216160255 36507222015 64 68719476704 68719474751 68719349759 68711350271 68199383039 35433480191