Office Applications and Entertainment, Magic Cubes  
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3.0 Magic Cubes (4 x 4 x 4)
Any number m = 0 ... 63 can be written as m = b_{1} + 4 * b_{2}
+ 16 * b_{3}
with b_{i} = 0, 1, 2, 3 for i = 1, 2, 3 (Quaternary representation).
3.16.1 Simple Magic Cubes, Horizontal Associated Magic Planes
Sudoku Comparable Magic Cubes, as defined above, can be obtained by applying the equations as deducted in Section 3.13.1, however for a Magic Sum 6.
The defined Magic Cubes can be generated by selecting combinations of Sudoku Comparable Cubes (B1, B2, B3) while ensuring that the resulting Cube C contains all integers 1 thru 64.
3.16.2 Simple Magic Cubes, Horizontal Pan Magic Planes (3DCompact)
Sudoku Comparable Magic Cubes, as defined above, can be obtained by applying the equations as deducted in Section 3.13.2, however for a Magic Sum 6.
The defined Magic Cubes can be generated by selecting combinations of Sudoku Comparable Cubes (B1, B2, B3) while ensuring that the resulting Cube C contains all integers 1 thru 64.
3.16.3 Simple Magic Cubes, Associated with Horizontal Magic Planes
Sudoku Comparable Magic Cubes, as defined above, can be obtained by applying the equations as deducted in Section 3.13.3, however for a Magic Sum 6.
The defined Magic Cubes can be generated by selecting combinations of Sudoku Comparable Cubes (B1, B2, B3) while ensuring that the resulting Cube C contains all integers 1 thru 64.
3.16.4 Simple Magic Cubes, Associated and 3DCompact
Sudoku Comparable Magic Cubes, as defined above, can be obtained by applying the equations as deducted in Section 3.13.4, however for a Magic Sum 6.
The defined Magic Cubes can be generated by selecting combinations of Sudoku Comparable Cubes (B1, B2, B3) while ensuring that the resulting Cube C contains all integers 1 thru 64.
3.16.5 Simple Magic Cubes, Plane Symmetrical
Sudoku Comparable Magic Cubes, as defined above, can be obtained by applying the equations as deducted in Section 3.13.5, however for a Magic Sum 6.
The corresponding Magic Cubes can be generated by selecting combinations of Sudoku Comparable Cubes (B1, B2, B3) while ensuring that the resulting Cube C contains all integers 1 thru 64.
3.16.6 Pantriagonal Magic Cubes, Complete
Quaternary Pantriagonal Complete Magic Cubes can be obtained by applying the equations deducted in Section 3.14.1, however for a Magic Sum 6.
3.16.7 Pantriagonal Magic Cubes, Complete, Horizontal Magic Planes
Quaternary Pantriagonal Magic Cubes, as defined above, can be obtained by applying the equations deducted in Section 3.14.2, however for a Magic Sum 6.
The obtained results regarding the miscellaneous types of order 4 Magic Cubes as deducted and discussed in previous sections are summarized in following table: 
Class
Main Characteristics
Method
Tag
Subroutine
Results
Simple
Horizontal Sym Magic Planes
Sudoku
B1/2/3
Attachment 3.16.1
36864Horizontal Pan Magic Planes
Sudoku
B1/2/3
Attachment 3.16.2
36864Associated, Hor. Magic Planes
Sudoku
B1/2/3
Attachment 3.16.3
49152Associated, 3DCompact
Sudoku
B1/2/3
Attachment 3.16.4
104448Plane Symmetrical
Hor Magic PlanesSudoku
B1/2/3
Attachment 3.16.5
18432Pantriagonal
Complete
Sudoku
B1/2/3
1536
34048 (Note 1)Complete, Hor. Magic Planes
Sudoku
B1/2/3
Attachment 3.16.7
135168
Note 1: Produced with B1 = constant.

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