What's Hot? by Kanji Setsuda
I have recently invented a new, unique way how to compose special types of magic squares of order 4, 8 and 9 and cubes of order 4. Read every article in Chapter 7.
1. First of all I found how to draw all possible 'Basic View Diagrams' for the developed forms of the same high dimensional Extra-Cubic Object. With these Basic Forms we could know how to define and compose our object solutions more accurately.
2. I actually designed and composed the 4- or 6-dimensional ECO of order 2 and 3 again with these new Basic Forms, and exactly knew how many solutions in all we could make for every object.
(1) 384 'primitive' solutions of ECO2^4:
.. (a) 48 standard solutions of Self-complementary magic squares of order 4;
.. (b) 48 standard solutions of Pan-diagonal magic squares of order 4;
.. (c) 48 standard solutions of 'Composite & Complete' pan-magic squares of order 4;
(2) 46080 'primitive' solutions of ECO2^6:
.. (a) 960 standard solutions of 'Composite & Complete' pan-magic cubes 4x4x4;
.. (b) 5760 standard solutions of 'Three-type Simultaneous' pan-magic squares 8x8: 'Composite', Pandiagonal and Self-complementary;
.. (c) 5760 standard solutions of multiple type of 'Composite & Complete' pan-magic squares 8x8 including 4 little squares 4x4 within.
(3) 22272 'primitive' solutions of ECO3^4:
.. 2784 standard solutions of Self-complementary 'Euler Squares' of order 9 including multiple little squares 3x3 within.
3. How many pictures in all can we draw for the different Basic View-Diagrams of the same developed high dimensional ECO?
(1) 384 'primitive' forms of ECO2^4: ... 4P4x2^4=24x16=384
(2) 46080 'primitive' forms of ECO2^6:. 6P6x2^6=720x64=46080
(3) 384 'primitive' forms of ECO3^4: ... 4P4x2^4=24x16=384
4. The count of Basic Forms is the same with the count of object solutions in the case (1) and (2) above. In the case (3) 384 may mean any different type of ECO from the case of 22272 primitive solutions of ECO. But why?
5. The Basic View Forms of our object we actually drew might be regarded as any 'Prototype Squares(or Cubes)', I thought. We might well use the 'DAM Transformation' method here, with which we might make the solutions directly from the Basic View Forms, I imagined.
6. I finally invented a new, unique method how to compose special object solutions, using all possible view forms of the developed ECO, and making them directly into the solutions by the 'Do-it-After-the-Model Transformation'.
What I have successfully composed by this method are:
(1) (a) 384 primitive solutions of Self-complementary magic squares of order 4;
... (b) 48 standard solutions of 'Composite & Complete' magic squares of order 4.
(2) (a) 960 standard solutions of 'Composite & Complete' magic cubes of order 4;
... (b) 5760 standard solutions of Three-type Simultaneous MS88: 'Composite', Self-complementary and Pan-diagonal.
(3) 48 standard solutions of 'Complete Euler' type of Self-complementary magic squares of order 9 including multiple little squares 3x3 within. This method is not only unique, but also very simple and quick.
7. I have invented some additional transformation systems how to compose some other famous types of object solutions, using all those methods mentioned above.
What I have successfully recomposed by these methods are:
(1) 6720 standard solutions of 'Composite and Pantriagonal' magic cubes 4x4x4;
(2) 368640 standard solutions of 'Composite & Complete' magic squares 8x8;
Each of these methods takes the only Model as an essential material at first, but make all the other solutions only by our unique, simple and quick methods afterward.
8. Positional number system of the base N is always essential to this method. What we can make with this method is only the 'Complete Euler Squares(and Cubes)' and also any developed form of high dimensional ECO at the same time.
9. I believe there is certainly a great 'internal relation' among everything: 'Positional number system of the base N', 'Complete Euler squares and cubes', 'High dimensional extra-cubic object', 'Prototype squares and cubes', and 'Do-it-After-the-Model Transformation'.
** Developed Diagrams for Extra-Cubic Objects of Order 2^4 **
** The Selected 4 View-Forms with 'Composite Conditions' **
1/d0 /d1 | n1+n2+n3+n4=C | n9+n10+n11+n12=C
1---- 2 9----10 | n1+n2+n5+n6=C | n9+n10+n13+n14=C
| 3--+- 4 | 11--+-12 | n1+n3+n5+n7=C | n9+n11+n13+n15=C
5--|- 6 | 13--|-14 | | n2+n4+n6+n8=C | n10+n12+n14+n16=C
7---- 8 15----16 | n3+n4+n7+n8=C | n11+n12+n15+n16=C
| n5+n6+n7+n8=C | n13+n14+n15+n16=C
2/d0 /d1 | n1+n2+n3+n4=C | n5+n6+n7+n8=C
1---- 2 5---- 6 | n1+n2+n9+n10=C | n5+n6+n13+n14=C
| 3--+- 4 | 7--+- 8 | n1+n3+n9+n11=C | n5+n7+n13+n15=C
9--|-10 | 13--|-14 | | n2+n4+n10+n12=C | n6+n8+n14+n16=C
11----12 15----16 | n3+n4+n11+n12=C | n7+n8+n15+n16=C
| n9+n10+n11+n12=C | n13+n14+n15+n16=C
3/d0 /d1 | n1+n2+n5+n6=C | n3+n4+n7+n8=C
1---- 2 3---- 4 | n1+n2+n9+n10=C | n3+n4+n11+n12=C
| 5--+- 6 | 7--+- 8 | n1+n5+n9+n13=C | n3+n7+n11+n15=C
9--|-10 | 11--|-12 | | n2+n6+n10+n14=C | n4+n8+n12+n16=C
13----14 15----16 | n5+n6+n13+n14=C | n7+n8+n15+n16=C
| n9+n10+n13+n14=C | n11+n12+n15+n16=C
4/d0 /d1 | n1+n3+n5+n7=C | n2+n4+n6+n8=C
1---- 3 2---- 4 | n1+n3+n9+n11=C | n2+n4+n10+n12=C
| 5--+- 7 | 6--+- 8 | n1+n5+n9+n13=C | n2+n6+n10+n14=C
9--|-11 | 10--|-12 | | n3+n7+n11+n15=C | n4+n8+n12+n16=C
13----15 14----16 | n5+n7+n13+n15=C | n6+n8+n14+n16=C
| n9+n11+n13+n15=C | n10+n12+n14+n16=C
** Collection of 'Composite Conditions' for The 12 Essential Ones **
n1+n2+n3+n4=C ...(1); n1+n2+n5+n6=C ...(2); n1+n2+n9+n10=C ...(3);
n1+n3+n5+n7=C ...(4); n1+n3+n9+n11=C ...(5); n1+n5+n9+n13=C ...(6);
n2+n4+n6+n8=C ...(7); n2+n4+n10+n12=C ...(8); n2+n6+n10+n14=C ...(9);
n3+n4+n7+n8=C ...(10); n3+n4+n11+n12=C ...(11); n5+n6+n7+n8=C ...(12);
** New Method of Composing 'S-C' and 'C.and.C' Magic Squares 4^2 **
** Using All Possible View-Forms of Developed E.C.Objects 2^4 **
[1]
P1/d0 /d1 SC/ CC/
1---- 2 3---- 4 1 2 3 4 1 2 4 3
| 9--+-10 | 11--+-12 5 6 7 8 5 6 8 7
5--|- 6 | 7--|- 8 | 9 10 11 12 13 14 16 15
13----14 15----16 13 14 15 16 9 10 12 11
EC/D2i
0--0 0--0 0--0 0--0 0--0 1--1 0--1 0--1
| 1--1 | 1--1 | 0--0 | 0--0 | 0--0 | 1--1 | 0--1 | 0--1
0-|0 | 0-|0 | 1-|1 | 1-|1 | 0-|0 | 1-|1 | 0-|1 | 0-|1 |
1--1 1--1 1--1 1--1 0--0 1--1 0--1 0--1
/2^3 /2^2 /2^1 /2^0
SC/D2i CC/D2i
0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0
0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0
1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0
1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0
/2^3 /^2 /^1 /^0 /2^3 /^2 /^1 /^0
S1/d0 /d1 SC/ CC/
1----15 14---- 4 1 15 14 4 1 15 4 14
| 8--+-10 | 11--+- 5 12 6 7 9 12 6 9 7
12--|- 6 | 7--|- 9 | 8 10 11 5 13 3 16 2
13---- 3 2----16 13 3 2 16 8 10 5 11
EC/D2i
0--1 1--0 0--1 1--0 0--1 0--1 0--0 1--1
| 0--1 | 1--0 | 1--0 | 0--1 | 1--0 | 1--0 | 1--1 | 0--0
1-|0 | 0-|1 | 0-|1 | 1-|0 | 1-|0 | 1-|0 | 1-|1 | 0-|0 |
1--0 0--1 1--0 0--1 0--1 0--1 0--0 1--1
/2^3 /2^2 /2^1 /2^0
SC/D2i CC/D2i
0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1
1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0
0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1
1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0
/2^3 /^2 /^1 /^0 /2^3 /^2 /^1 /^0
[2]
P2/d0 /d1 SC/ CC/
1---- 2 5---- 6 1 2 5 6 1 2 6 5
| 9--+-10 | 13--+-14 3 4 7 8 3 4 8 7
3--|- 4 | 7--|- 8 | 9 10 13 14 11 12 16 15
11----12 15----16 11 12 15 16 9 10 14 13
EC/D2i
0--0 0--0 0--0 1--1 0--0 0--0 0--1 0--1
| 1--1 | 1--1 | 0--0 | 1--1 | 0--0 | 0--0 | 0--1 | 0--1
0-|0 | 0-|0 | 0-|0 | 1-|1 | 1-|1 | 1-|1 | 0-|1 | 0-|1 |
1--1 1--1 0--0 1--1 1--1 1--1 0--1 0--1
/2^3 /2^2 /2^1 /2^0
SC/D2i CC/D2i
0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0
0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0
1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0
1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0
/2^3 /^2 /^1 /^0 /2^3 /^2 /^1 /^0
S2/d0 /d1 SC/ CC/
1----15 12---- 6 1 15 12 6 1 15 6 12
| 8--+-10 | 13--+- 3 14 4 7 9 14 4 9 7
14--|- 4 | 7--|- 9 | 8 10 13 3 11 5 16 2
11---- 5 2----16 11 5 2 16 8 10 3 13
EC/D2i
0--1 1--0 0--1 0--1 0--1 1--0 0--0 1--1
| 0--1 | 1--0 | 1--0 | 1--0 | 1--0 | 0--1 | 1--1 | 0--0
1-|0 | 0-|1 | 1-|0 | 1-|0 | 0-|1 | 1-|0 | 1-|1 | 0-|0 |
1--0 0--1 0--1 0--1 1--0 0--1 0--0 1--1
/2^3 /2^2 /2^1 /2^0
SC/D2i CC/D2i
0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1
1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0
0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1
1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0
/2^3 /^2 /^1 /^0 /2^3 /^2 /^1 /^0
[3]
P3/d0 /d1 SC/ CC/
1---- 2 9----10 1 2 9 10 1 2 10 9
| 5--+- 6 | 13--+-14 3 4 11 12 3 4 12 11
3--|- 4 | 11--|-12 | 5 6 13 14 7 8 16 15
7---- 8 15----16 7 8 15 16 5 6 14 13
EC/D2i
0--0 1--1 0--0 0--0 0--0 0--0 0--1 0--1
| 0--0 | 1--1 | 1--1 | 1--1 | 0--0 | 0--0 | 0--1 | 0--1
0-|0 | 1-|1 | 0-|0 | 0-|0 | 1-|1 | 1-|1 | 0-|1 | 0-|1 |
0--0 1--1 1--1 1--1 1--1 1--1 0--1 0--1
/2^3 /2^2 /2^1 /2^0
SC/D2i CC/D2i
0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0
0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0
0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0
0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0
/2^3 /^2 /^1 /^0 /2^3 /^2 /^1 /^0
S3/d0 /d1 SC/ CC/
1----15 8----10 1 15 8 10 1 15 10 8
| 12--+- 6 | 13--+- 3 14 4 11 5 14 4 5 11
14--|- 4 | 11--|- 5 | 12 6 13 3 7 9 16 2
7---- 9 2----16 7 9 2 16 12 6 3 13
EC/D2i
0--1 0--1 0--1 1--0 0--1 1--0 0--0 1--1
| 1--0 | 1--0 | 0--1 | 1--0 | 1--0 | 0--1 | 1--1 | 0--0
1-|0 | 1-|0 | 1-|0 | 0-|1 | 0-|1 | 1-|0 | 1-|1 | 0-|0 |
0--1 0--1 1--0 0--1 1--0 0--1 0--0 1--1
/2^3 /2^2 /2^1 /2^0
SC/D2i CC/D2i
0 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1
1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0
1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1
0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0
/2^3 /^2 /^1 /^0 /2^3 /^2 /^1 /^0
** New Method of Composing Special Magic Cubes 4^3 and Squares 8^2 **
** Using All Possible View-Forms of Developed E.C.Objects of 2^6 **
** Basic View-Diagram of Developed ECO2^6 #1 **
1---------- 2---------- 3---------- 4 SC4^3/8^2
| 17 18 19 | 20 1 2 3 4 17 18 19 20
5 33 6 34 7 35 8 36 5 6 7 8 21 22 23 24
| 21 49----22----50----23----51--+-24----52 9 10 11 12 25 26 27 28
9 37 | 10 38 11 39 12 40 | 13 14 15 16 29 30 31 32
| 25 53 26 54 27 55 | 28 56 33 34 35 36 49 50 51 52
13----41--|-14----42----15----43----16 44 | 37 38 39 40 53 54 55 56
29 57 30 58 31 59 32 60 41 42 43 44 57 58 59 60
45 | 46 47 48 | 45 46 47 48 61 62 63 64
61----------62----------63----------64
** Representative 'Model' Solution **
1----------63----------62---------- 4 SC4^3/8^2
| 48 18 19 | 45 1 63 62 4 48 18 19 45
60 32 6 34 7 35 57 29 60 6 7 57 21 43 42 24
| 21 49----43----15----42----14--+-24----52 56 10 11 53 25 39 38 28
56 37 | 10 27 11 26 53 40 | 13 51 50 16 36 30 31 33
| 25 12 39 54 38 55 | 28 9 32 34 35 29 49 15 14 52
13----41--|-51----23----50----22----16 44 | 37 27 26 40 12 54 55 9
36 8 30 58 31 59 33 5 41 23 22 44 8 58 59 5
20 | 46 47 17 | 20 46 47 17 61 3 2 64
61---------- 3---------- 2----------64
** Type Conversion of S-C type into 'C.and.C' Solution **
1----------63---------- 4----------62 CC4^3/8^2
| 48 18 45 | 19 1 63 4 62 36 30 33 31
60 49 6 15 57 52 7 14 60 6 57 7 25 39 28 38
| 21 32----43----34----24----29--+-42----35 13 51 16 50 48 18 45 19
13 12 | 51 54 16 9 50 55 | 56 10 53 11 21 43 24 42
| 36 37 30 27 33 40 | 31 26 29 35 32 34 64 2 61 3
56----61--|-10---- 3----53----64----11 2 | 40 26 37 27 5 59 8 58
25 20 39 46 28 17 38 47 17 47 20 46 52 14 49 15
8 | 58 5 59 | 44 22 41 23 9 55 12 54
41----------23----------44----------22
** Basic View-Diagram of Developed ECO2^6 #2 **
[1] P1/EC2^6
1---- 2 3---- 4 33----34 35----36
| 5--+- 6 | 7--+- 8 | 37--+-38 | 39--+-40
9--|-10 | 11--|-12 | 41--|-42 | 43--|-44 |
13----14 15----16 45----46 47----48
17----18 19----20 49----50 51----52
| 21--+-22 | 23--+-24 | 53--+-54 | 55--+-56
25--|-26 | 27--|-28 | 57--|-58 | 59--|-60 |
29----30 31----32 61----62 63----64
P1/ /D2i
1 2 3 4 5 6 7 8 00000000 00000000 00000000 00001111 00110011 01010101
9 10 11 12 13 14 15 16 00000000 00000000 11111111 00001111 00110011 01010101
17 18 19 20 21 22 23 24 00000000 11111111 00000000 00001111 00110011 01010101
25 26 27 28 29 30 31 32 00000000 11111111 11111111 00001111 00110011 01010101
33 34 35 36 37 38 39 40 11111111 00000000 00000000 00001111 00110011 01010101
41 42 43 44 45 46 47 48 11111111 00000000 11111111 00001111 00110011 01010101
49 50 51 52 53 54 55 56 11111111 11111111 00000000 00001111 00110011 01010101
57 58 59 60 61 62 63 64 11111111 11111111 11111111 00001111 00110011 01010101
/2^5 /^4 /^3 /^2 /^1 /^0
** Representative 'Model' Solution **
S1/EC2^6
1----63 62---- 4 32----34 35----29
| 60--+- 6 | 7--+-57 | 37--+-27 | 26--+-40
56--|-10 | 11--|-53 | 41--|-23 | 22--|-44 |
13----51 50----16 20----46 47----17
48----18 19----45 49----15 14----52
| 21--+-43 | 42--+-24 | 12--+-54 | 55--+- 9
25--|-39 | 38--|-28 | 8--|-58 | 59--|- 5 |
36----30 31----33 61---- 3 2----64
S1/ /D2i
1 63 4 62 6 60 7 57 01010101 01010101 01010101 01011010 01100110 00111100
56 10 53 11 51 13 50 16 10101010 10101010 01010101 10100101 10011001 11000011
25 39 28 38 30 36 31 33 01010101 10101010 10101010 01011010 01100110 00111100
48 18 45 19 43 21 42 24 10101010 01010101 10101010 10100101 10011001 11000011
41 23 44 22 46 20 47 17 10101010 01010101 10101010 01011010 01100110 00111100
32 34 29 35 27 37 26 40 01010101 10101010 10101010 10100101 10011001 11000011
49 15 52 14 54 12 55 9 10101010 10101010 01010101 01011010 01100110 00111100
8 58 5 59 3 61 2 64 01010101 01010101 01010101 10100101 10011001 11000011
/2^5 /^4 /^3 /^2 /^1 /^0
** Basic View-Diagram and Sample Solution of Developed ECO3^4 **
[BD]
1----- 2----- 3 4----- 5----- 6 7----- 8----- 9
|10 11 |12 |13 14 |15 |16 17 |18
28 19-29--20-30--21 31 22-32--23-33--24 34 25-35--26-36--27
|37 | 38 |39 | |40 | 41 |42 | |43 | 44 |45 |
55--46-56--47-57 48 58--49-59--50-60 51 61--52-62--53-63 54
64 | 65 66 | 67 | 68 69 | 70 | 71 72 |
73-----74-----75 76-----77-----78 79-----80-----81
N3i/
0000 0001 0002 0010 0011 0012 0020 0021 0022
0100 0101 0102 0110 0111 0112 0120 0121 0122
0200 0201 0202 0210 0211 0212 0220 0221 0222
1000 1001 1002 1010 1011 1012 1020 1021 1022
1100 1101 1102 1110 1111 1112 1120 1121 1122
1200 1201 1202 1210 1211 1212 1220 1221 1222
2000 2001 2002 2010 2011 2012 2020 2021 2022
2100 2101 2102 2110 2111 2112 2120 2121 2122
2200 2201 2202 2210 2211 2212 2220 2221 2222
ED/ /D3i
1 2 3 4 5 6 7 8 9 000000000 000000000 000111222 012012012
10 11 12 13 14 15 16 17 18 000000000 111111111 000111222 012012012
19 20 21 22 23 24 25 26 27 000000000 222222222 000111222 012012012
28 29 30 31 32 33 34 35 36 111111111 000000000 000111222 012012012
37 38 39 40 41 42 43 44 45 111111111 111111111 000111222 012012012
46 47 48 49 50 51 52 53 54 111111111 222222222 000111222 012012012
55 56 57 58 59 60 61 62 63 222222222 000000000 000111222 012012012
64 65 66 67 68 69 70 71 72 222222222 111111111 000111222 012012012
73 74 75 76 77 78 79 80 81 222222222 222222222 000111222 012012012
** Representative 'Model' Solution **
SS1/
1-----54-----68 72----- 5-----46 50-----64----- 9
|78 11 |34 |29 79 |15 |16 33 |74
80 44-13--58-30--21 31 22-75--39-17--62 12 57-35--26-76--40
|37 | 63 |23 | |27 | 41 |55 | |59 | 19 |45 |
42-- 6-56--47-25 70 20--65-43-- 7-60 51 61--52-24--69-38 2
8 | 49 66 | 67 | 3 53 | 48 | 71 4 |
73-----18-----32 36-----77-----10 14-----28-----81
1/ /D3i
1 54 68 72 5 46 50 64 9 012201120 021102210 021210102 021210102
78 11 34 29 79 15 16 33 74 201120012 210021102 102021210 210102021
44 58 21 22 39 62 57 26 40 120012201 102210021 210102021 102021210
80 13 30 31 75 17 12 35 76 201120012 210021102 210102021 102021210
37 63 23 27 41 55 59 19 45 120012201 102210021 021210102 021210102
6 47 70 65 7 51 52 69 2 012201120 021102210 102021210 210102021
42 56 25 20 43 60 61 24 38 120012201 102210021 102021210 210102021
8 49 66 67 3 53 48 71 4 012201120 021102210 210102021 102021210
73 18 32 36 77 10 14 28 81 201120012 210021102 021210102 021210102
** Making Some Other Larger Sets of Object Solutions **
.-------------------------------------.
| .--> |
.----------------. |.------------|---. |
| All Possible | || "Composite & | "Composite & |
| View Diagrams | || Complete" type | Pan-triagonal |
| of Extra-cubic --------> of Magic Cubes --> type of Magic |
| magic objects | DAM || of order 4 | Cubes of order 4 |
| of Order 2^6 |Trans-||(46080 Primitive| (6720 Standard |
| (46080 Forms) |forma-|| Solutions) | Solutions) |
'----------------' tion |'------------|---' |
| V |
| by additional Transformation System |
'-------------------------------------'
.----------------------------------------.
| .--> |
.----------------. |.------------|---. |
| All Possible | || Multiple 4x4 | Standard type of |
| View Diagrams | || Type of 'C&C' |'Composite & Complete'|
| of Extra-cubic --------> Pan-Magic --> Pan-Magic Squares |
| magic objects | DAM || Squares 8x8 | 8x8 |
| of Order 2^6 |Trans-||(46080 Primitive| (368640 Standard |
| (46080 Forms) |forma-|| Solutions) | Solutions) |
'----------------' tion |'------------|---' |
| V |
| by additional Transformation System |
'----------------------------------------'
(on May 22, 2005 and Feb. 5, 2009; Kanji Setsuda)
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