• Magic Cube

  Overview Magic Squares Magic Cubes Magic Hypercubes
  • Order-2^p Tesseracts Prime Order Tesseracts 5-D Hypercube n-Dimensions
    • 6-D Master Base Lines
  Other Order-8 Cubes Miscellaneous

6-D MASTER BASE LINES

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 55^th row, 20^th column, 3^rd pillar, 34^th file, 16^th 5-D, and 45^th 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.