The Magic Encyclopedia ™


Pandiagonal Compact Complete Squares Order 8
(by Aale de Winkel)
NOTE: preliminary upload to be verified


<Arie Breedijk> allerted me to http://www.f1compiler.com/samples/samples.html where complete listings of the results of iterations for the {compact complete} as well as the {Franklin} order 8 magic squares can be found. Analysis of the {pandiagonal} shows the both the {pandiagonal compact complete} as well as the {pandiagonal Franklin} has a total 368640 (= 360 * 1024) squares, of which 23040 with 0 in the topleft corner.
The pairwise interchange of every other column / row (ie _x[0,3,2,1,4,7,6,5] and _x[2,1,0,3,6,5,4,7]; x=1,2) though the latter one doesn't leave the position [0,0] on its place but combining with panrelocation (in the form of monagonal permutation) [0,0] and {pandiagonal compact complete} monagonal permutations could be found (monagonal permutation groups of order 16, combined into a group of 256) which when utilized resulted in 90 different sets (90 * 256 = 23040).
Further analisis shows that component permutation between the four bits numbers possible at position [1,0] combine with component permutations #[perm(0,1),perm(2,..,5)] into doubling of the squares (given mentioned monagonal permutation group) so half of the 24 permutations are needed. The high bits interchange (perm(0,1)) turns 16 into 32 which monagonally permutes to [6,0]. combining with the four bits permutation 30 squares remain. So 60 squares stemming from #[0,1,perm(2,..,5)] and 30 from #[1,0,perm(2,..,5)]
The listed binary components show the the square nicely constructs with the Dwane Campbel construction method
The spreadsheet PandiagonalSquaresOrder08.xlsx I developed in support of the below

Order08PandiagonalCompactComplete.html
compactcomplete

00 15 16 31 49 62 33 46
51 60 35 44 02 13 18 29
04 11 20 27 53 58 37 42
55 56 39 40 06 09 22 25
14 01 30 17 63 48 47 32
61 50 45 34 12 03 28 19
10 05 26 21 59 52 43 36
57 54 41 38 08 07 24 23
fourbitperm

0 1 2 3 4 5
0 2 1 3 4 5
0 3 2 1 4 5
0 4 2 3 1 5
0 5 2 3 4 1
generators

[0,1,2,3,4,5,6,7]
[0,1,2,7,4,5,6,3]
[0,1,6,3,4,5,2,7]
[0,5,6,7,4,1,2,3]
[1,2,3,0,5,6,7,4]
[1,2,7,4,5,6,3,0]
[2,3,0,1,6,7,4,5]
{panmagic compact complete} invariant monagonal permutations
generatored by the above 'generators' (at least when applied in mentioned order)
[0,1,2,3,4,5,6,7]
[0,1,2,7,4,5,6,3]
[0,1,6,3,4,5,2,7]
[0,1,6,7,4,5,2,3]
[0,3,2,1,4,7,6,5]
[0,3,2,5,4,7,6,1]
[0,3,6,1,4,7,2,5]
[0,3,6,5,4,7,2,1]
[0,5,2,3,4,1,6,7]
[0,5,2,7,4,1,6,3]
[0,5,6,3,4,1,2,7]
[0,5,6,7,4,1,2,3]
[0,7,2,1,4,3,6,5]
[0,7,2,5,4,3,6,1]
[0,7,6,1,4,3,2,5]
[0,7,6,5,4,3,2,1]
[1,0,3,2,5,4,7,6]
[1,0,3,6,5,4,7,2]
[1,0,7,2,5,4,3,6]
[1,0,7,6,5,4,3,2]
[1,2,3,0,5,6,7,4]
[1,2,3,4,5,6,7,0]
[1,2,7,0,5,6,3,4]
[1,2,7,4,5,6,3,0]
[1,4,3,2,5,0,7,6]
[1,4,3,6,5,0,7,2]
[1,4,7,2,5,0,3,6]
[1,4,7,6,5,0,3,2]
[1,6,3,0,5,2,7,4]
[1,6,3,4,5,2,7,0]
[1,6,7,0,5,2,3,4]
[1,6,7,4,5,2,3,0]
[2,1,0,3,6,5,4,7]
[2,1,0,7,6,5,4,3]
[2,1,4,3,6,5,0,7]
[2,1,4,7,6,5,0,3]
[2,3,0,1,6,7,4,5]
[2,3,0,5,6,7,4,1]
[2,3,4,1,6,7,0,5]
[2,3,4,5,6,7,0,1]
[2,5,0,3,6,1,4,7]
[2,5,0,7,6,1,4,3]
[2,5,4,3,6,1,0,7]
[2,5,4,7,6,1,0,3]
[2,7,0,1,6,3,4,5]
[2,7,0,5,6,3,4,1]
[2,7,4,1,6,3,0,5]
[2,7,4,5,6,3,0,1]
[3,0,1,2,7,4,5,6]
[3,0,1,6,7,4,5,2]
[3,0,5,2,7,4,1,6]
[3,0,5,6,7,4,1,2]
[3,2,1,0,7,6,5,4]
[3,2,1,4,7,6,5,0]
[3,2,5,0,7,6,1,4]
[3,2,5,4,7,6,1,0]
[3,4,1,2,7,0,5,6]
[3,4,1,6,7,0,5,2]
[3,4,5,2,7,0,1,6]
[3,4,5,6,7,0,1,2]
[3,6,1,0,7,2,5,4]
[3,6,1,4,7,2,5,0]
[3,6,5,0,7,2,1,4]
[3,6,5,4,7,2,1,0]
[4,1,2,3,0,5,6,7]
[4,1,2,7,0,5,6,3]
[4,1,6,3,0,5,2,7]
[4,1,6,7,0,5,2,3]
[4,3,2,1,0,7,6,5]
[4,3,2,5,0,7,6,1]
[4,3,6,1,0,7,2,5]
[4,3,6,5,0,7,2,1]
[4,5,2,3,0,1,6,7]
[4,5,2,7,0,1,6,3]
[4,5,6,3,0,1,2,7]
[4,5,6,7,0,1,2,3]
[4,7,2,1,0,3,6,5]
[4,7,2,5,0,3,6,1]
[4,7,6,1,0,3,2,5]
[4,7,6,5,0,3,2,1]
[5,0,3,2,1,4,7,6]
[5,0,3,6,1,4,7,2]
[5,0,7,2,1,4,3,6]
[5,0,7,6,1,4,3,2]
[5,2,3,0,1,6,7,4]
[5,2,3,4,1,6,7,0]
[5,2,7,0,1,6,3,4]
[5,2,7,4,1,6,3,0]
[5,4,3,2,1,0,7,6]
[5,4,3,6,1,0,7,2]
[5,4,7,2,1,0,3,6]
[5,4,7,6,1,0,3,2]
[5,6,3,0,1,2,7,4]
[5,6,3,4,1,2,7,0]
[5,6,7,0,1,2,3,4]
[5,6,7,4,1,2,3,0]
[6,1,0,3,2,5,4,7]
[6,1,0,7,2,5,4,3]
[6,1,4,3,2,5,0,7]
[6,1,4,7,2,5,0,3]
[6,3,0,1,2,7,4,5]
[6,3,0,5,2,7,4,1]
[6,3,4,1,2,7,0,5]
[6,3,4,5,2,7,0,1]
[6,5,0,3,2,1,4,7]
[6,5,0,7,2,1,4,3]
[6,5,4,3,2,1,0,7]
[6,5,4,7,2,1,0,3]
[6,7,0,1,2,3,4,5]
[6,7,0,5,2,3,4,1]
[6,7,4,1,2,3,0,5]
[6,7,4,5,2,3,0,1]
[7,0,1,2,3,4,5,6]
[7,0,1,6,3,4,5,2]
[7,0,5,2,3,4,1,6]
[7,0,5,6,3,4,1,2]
[7,2,1,0,3,6,5,4]
[7,2,1,4,3,6,5,0]
[7,2,5,0,3,6,1,4]
[7,2,5,4,3,6,1,0]
[7,4,1,2,3,0,5,6]
[7,4,1,6,3,0,5,2]
[7,4,5,2,3,0,1,6]
[7,4,5,6,3,0,1,2]
[7,6,1,0,3,2,5,4]
[7,6,1,4,3,2,5,0]
[7,6,5,0,3,2,1,4]
[7,6,5,4,3,2,1,0]
Binary components
DC(0F^55,3C^55,55^0F,55^3C,55^5A,5A^55)
Octary components
0F^55

0 0 0 0 1 1 1 1
1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 1
1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 1
1 1 1 1 0 0 0 0
0 0 0 0 1 1 1 1
1 1 1 1 0 0 0 0
3C^55

0 0 1 1 1 1 0 0
1 1 0 0 0 0 1 1
0 0 1 1 1 1 0 0
1 1 0 0 0 0 1 1
0 0 1 1 1 1 0 0
1 1 0 0 0 0 1 1
0 0 1 1 1 1 0 0
1 1 0 0 0 0 1 1
55^0F

0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
0 1 2 3 6 7 4 5
6 7 4 5 0 1 2 3
0 1 2 3 6 7 4 5
6 7 4 5 0 1 2 3
1 0 3 2 7 6 5 4
7 6 5 4 1 0 3 2
1 0 3 2 7 6 5 4
7 6 5 4 1 0 3 2
55^3C

0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
0 1 0 1 0 1 0 1
55^5A

0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
1 0 1 0 1 0 1 0
0 1 0 1 0 1 0 1
5A^55

0 1 0 1 1 0 1 0
1 0 1 0 0 1 0 1
0 1 0 1 1 0 1 0
1 0 1 0 0 1 0 1
0 1 0 1 1 0 1 0
1 0 1 0 0 1 0 1
0 1 0 1 1 0 1 0
1 0 1 0 0 1 0 1
0 7 0 7 1 6 1 6
3 4 3 4 2 5 2 5
4 3 4 3 5 2 5 2
7 0 7 0 6 1 6 1
6 1 6 1 7 0 7 0
5 2 5 2 4 3 4 3
2 5 2 5 3 4 3 4
1 6 1 6 0 7 0 7

hereunder a listing of the 90 lowest member of each set of squares
The list is compiled by using all 720 component permutations and combining the monagonal permutation (of type _x[0,perm(1..7)]) and test for the lowest obtainable. Permutations were combined as far as possible and the possible transposing (^[1,0]) positioned toward the end of the component permutation, but can be moved toward its front since the operations commute (ie #[perm(0..5)]^[perm(0,1)] = ^[perm(0,1)]#[perm(0..5)]) monagonal permution change of course direction (pe _1[perm(0..7)]^[perm(0,1)] = ^[perm(0,1)]_2[perm(0..7)]) rules obviously seen I reckon and used, further the monagonal permutations obviously can interchange an combine when equal into a diagonal permutation.

Order08PandiagonalCompactComplete.html
000 compactcomplete

00 15 16 31 49 62 33 46
51 60 35 44 02 13 18 29
04 11 20 27 53 58 37 42
55 56 39 40 06 09 22 25
14 01 30 17 63 48 47 32
61 50 45 34 12 03 28 19
10 05 26 21 59 52 43 36
57 54 41 38 08 07 24 23
001 compactcomplete
#[0,1,3,2,4,5]
_2[0,1,6,7,4,5,2,3]

00 15 16 31 49 62 33 46
51 60 35 44 02 13 18 29
06 09 22 25 55 56 39 40
53 58 37 42 04 11 20 27
14 01 30 17 63 48 47 32
61 50 45 34 12 03 28 19
08 07 24 23 57 54 41 38
59 52 43 36 10 05 26 21
002 compactcomplete
#[0,1,2,4,3,5]

00 15 16 31 49 62 33 46
53 58 37 42 04 11 20 27
02 13 18 29 51 60 35 44
55 56 39 40 06 09 22 25
14 01 30 17 63 48 47 32
59 52 43 36 10 05 26 21
12 03 28 19 61 50 45 34
57 54 41 38 08 07 24 23
003 compactcomplete
#[0,1,2,3,5,4]

00 15 16 31 50 61 34 45
51 60 35 44 01 14 17 30
04 11 20 27 54 57 38 41
55 56 39 40 05 10 21 26
13 02 29 18 63 48 47 32
62 49 46 33 12 03 28 19
09 06 25 22 59 52 43 36
58 53 42 37 08 07 24 23
004 compactcomplete
#[0,1,3,2,5,4]
_2[0,1,6,7,4,5,2,3]

00 15 16 31 50 61 34 45
51 60 35 44 01 14 17 30
05 10 21 26 55 56 39 40
54 57 38 41 04 11 20 27
13 02 29 18 63 48 47 32
62 49 46 33 12 03 28 19
08 07 24 23 58 53 42 37
59 52 43 36 09 06 25 22
005 compactcomplete
#[0,1,2,5,3,4]

00 15 16 31 50 61 34 45
54 57 38 41 04 11 20 27
01 14 17 30 51 60 35 44
55 56 39 40 05 10 21 26
13 02 29 18 63 48 47 32
59 52 43 36 09 06 25 22
12 03 28 19 62 49 46 33
58 53 42 37 08 07 24 23
006 compactcomplete
#[0,1,2,4,5,3]

00 15 16 31 52 59 36 43
53 58 37 42 01 14 17 30
02 13 18 29 54 57 38 41
55 56 39 40 03 12 19 28
11 04 27 20 63 48 47 32
62 49 46 33 10 05 26 21
09 06 25 22 61 50 45 34
60 51 44 35 08 07 24 23
007 compactcomplete
#[0,1,4,2,5,3]
_2[0,1,6,7,4,5,2,3]

00 15 16 31 52 59 36 43
53 58 37 42 01 14 17 30
03 12 19 28 55 56 39 40
54 57 38 41 02 13 18 29
11 04 27 20 63 48 47 32
62 49 46 33 10 05 26 21
08 07 24 23 60 51 44 35
61 50 45 34 09 06 25 22
008 compactcomplete
#[0,1,2,5,4,3]

00 15 16 31 52 59 36 43
54 57 38 41 02 13 18 29
01 14 17 30 53 58 37 42
55 56 39 40 03 12 19 28
11 04 27 20 63 48 47 32
61 50 45 34 09 06 25 22
10 05 26 21 62 49 46 33
60 51 44 35 08 07 24 23
009 compactcomplete
#[0,1,3,4,5,2]

00 15 16 31 56 55 40 39
57 54 41 38 01 14 17 30
02 13 18 29 58 53 42 37
59 52 43 36 03 12 19 28
07 08 23 24 63 48 47 32
62 49 46 33 06 09 22 25
05 10 21 26 61 50 45 34
60 51 44 35 04 11 20 27
010 compactcomplete
#[0,1,4,3,5,2]
_2[0,1,6,7,4,5,2,3]

00 15 16 31 56 55 40 39
57 54 41 38 01 14 17 30
03 12 19 28 59 52 43 36
58 53 42 37 02 13 18 29
07 08 23 24 63 48 47 32
62 49 46 33 06 09 22 25
04 11 20 27 60 51 44 35
61 50 45 34 05 10 21 26
011 compactcomplete
#[0,1,3,5,4,2]

00 15 16 31 56 55 40 39
58 53 42 37 02 13 18 29
01 14 17 30 57 54 41 38
59 52 43 36 03 12 19 28
07 08 23 24 63 48 47 32
61 50 45 34 05 10 21 26
06 09 22 25 62 49 46 33
60 51 44 35 04 11 20 27
012 compactcomplete
#[1,0,2,3,4,5]
_1[0,1,6,7,4,5,2,3]

00 15 17 30 49 62 32 47
51 60 34 45 02 13 19 28
04 11 21 26 53 58 36 43
55 56 38 41 06 09 23 24
14 01 31 16 63 48 46 33
61 50 44 35 12 03 29 18
10 05 27 20 59 52 42 37
57 54 40 39 08 07 25 22
013 compactcomplete
#[1,0,3,2,4,5]
_3[0,1,6,7,4,5,2,3]

00 15 17 30 49 62 32 47
51 60 34 45 02 13 19 28
06 09 23 24 55 56 38 41
53 58 36 43 04 11 21 26
14 01 31 16 63 48 46 33
61 50 44 35 12 03 29 18
08 07 25 22 57 54 40 39
59 52 42 37 10 05 27 20
014 compactcomplete
#[1,0,2,4,3,5]
_1[0,1,6,7,4,5,2,3]

00 15 17 30 49 62 32 47
53 58 36 43 04 11 21 26
02 13 19 28 51 60 34 45
55 56 38 41 06 09 23 24
14 01 31 16 63 48 46 33
59 52 42 37 10 05 27 20
12 03 29 18 61 50 44 35
57 54 40 39 08 07 25 22
015 compactcomplete
#[1,0,2,3,5,4]
_1[0,1,6,7,4,5,2,3]

00 15 18 29 50 61 32 47
51 60 33 46 01 14 19 28
04 11 22 25 54 57 36 43
55 56 37 42 05 10 23 24
13 02 31 16 63 48 45 34
62 49 44 35 12 03 30 17
09 06 27 20 59 52 41 38
58 53 40 39 08 07 26 21
016 compactcomplete
#[1,0,3,2,5,4]
_3[0,1,6,7,4,5,2,3]

00 15 18 29 50 61 32 47
51 60 33 46 01 14 19 28
05 10 23 24 55 56 37 42
54 57 36 43 04 11 22 25
13 02 31 16 63 48 45 34
62 49 44 35 12 03 30 17
08 07 26 21 58 53 40 39
59 52 41 38 09 06 27 20
017 compactcomplete
#[1,0,2,5,3,4]
_1[0,1,6,7,4,5,2,3]

00 15 18 29 50 61 32 47
54 57 36 43 04 11 22 25
01 14 19 28 51 60 33 46
55 56 37 42 05 10 23 24
13 02 31 16 63 48 45 34
59 52 41 38 09 06 27 20
12 03 30 17 62 49 44 35
58 53 40 39 08 07 26 21
018 compactcomplete
#[1,0,2,4,5,3]
_1[0,1,6,7,4,5,2,3]

00 15 20 27 52 59 32 47
53 58 33 46 01 14 21 26
02 13 22 25 54 57 34 45
55 56 35 44 03 12 23 24
11 04 31 16 63 48 43 36
62 49 42 37 10 05 30 17
09 06 29 18 61 50 41 38
60 51 40 39 08 07 28 19
019 compactcomplete
#[1,0,4,2,5,3]
_3[0,1,6,7,4,5,2,3]

00 15 20 27 52 59 32 47
53 58 33 46 01 14 21 26
03 12 23 24 55 56 35 44
54 57 34 45 02 13 22 25
11 04 31 16 63 48 43 36
62 49 42 37 10 05 30 17
08 07 28 19 60 51 40 39
61 50 41 38 09 06 29 18
020 compactcomplete
#[1,0,2,5,4,3]
_1[0,1,6,7,4,5,2,3]

00 15 20 27 52 59 32 47
54 57 34 45 02 13 22 25
01 14 21 26 53 58 33 46
55 56 35 44 03 12 23 24
11 04 31 16 63 48 43 36
61 50 41 38 09 06 29 18
10 05 30 17 62 49 42 37
60 51 40 39 08 07 28 19
021 compactcomplete
#[1,0,3,4,5,2]
_1[0,1,6,7,4,5,2,3]

00 15 24 23 56 55 32 47
57 54 33 46 01 14 25 22
02 13 26 21 58 53 34 45
59 52 35 44 03 12 27 20
07 08 31 16 63 48 39 40
62 49 38 41 06 09 30 17
05 10 29 18 61 50 37 42
60 51 36 43 04 11 28 19
022 compactcomplete
#[1,0,4,3,5,2]
_3[0,1,6,7,4,5,2,3]

00 15 24 23 56 55 32 47
57 54 33 46 01 14 25 22
03 12 27 20 59 52 35 44
58 53 34 45 02 13 26 21
07 08 31 16 63 48 39 40
62 49 38 41 06 09 30 17
04 11 28 19 60 51 36 43
61 50 37 42 05 10 29 18
023 compactcomplete
#[1,0,3,5,4,2]
_1[0,1,6,7,4,5,2,3]

00 15 24 23 56 55 32 47
58 53 34 45 02 13 26 21
01 14 25 22 57 54 33 46
59 52 35 44 03 12 27 20
07 08 31 16 63 48 39 40
61 50 37 42 05 10 29 18
06 09 30 17 62 49 38 41
60 51 36 43 04 11 28 19
024 compactcomplete
#[0,2,1,3,4,5]

00 23 08 31 41 62 33 54
43 60 35 52 02 21 10 29
04 19 12 27 45 58 37 50
47 56 39 48 06 17 14 25
22 01 30 09 63 40 55 32
61 42 53 34 20 03 28 11
18 05 26 13 59 44 51 36
57 46 49 38 16 07 24 15
025 compactcomplete
#[0,2,3,1,4,5]
_2[0,1,6,7,4,5,2,3]

00 23 08 31 41 62 33 54
43 60 35 52 02 21 10 29
06 17 14 25 47 56 39 48
45 58 37 50 04 19 12 27
22 01 30 09 63 40 55 32
61 42 53 34 20 03 28 11
16 07 24 15 57 46 49 38
59 44 51 36 18 05 26 13
026 compactcomplete
#[0,2,1,4,3,5]

00 23 08 31 41 62 33 54
45 58 37 50 04 19 12 27
02 21 10 29 43 60 35 52
47 56 39 48 06 17 14 25
22 01 30 09 63 40 55 32
59 44 51 36 18 05 26 13
20 03 28 11 61 42 53 34
57 46 49 38 16 07 24 15
027 compactcomplete
#[0,2,1,3,5,4]

00 23 08 31 42 61 34 53
43 60 35 52 01 22 09 30
04 19 12 27 46 57 38 49
47 56 39 48 05 18 13 26
21 02 29 10 63 40 55 32
62 41 54 33 20 03 28 11
17 06 25 14 59 44 51 36
58 45 50 37 16 07 24 15
028 compactcomplete
#[0,2,3,1,5,4]
_2[0,1,6,7,4,5,2,3]

00 23 08 31 42 61 34 53
43 60 35 52 01 22 09 30
05 18 13 26 47 56 39 48
46 57 38 49 04 19 12 27
21 02 29 10 63 40 55 32
62 41 54 33 20 03 28 11
16 07 24 15 58 45 50 37
59 44 51 36 17 06 25 14
029 compactcomplete
#[0,2,1,5,3,4]

00 23 08 31 42 61 34 53
46 57 38 49 04 19 12 27
01 22 09 30 43 60 35 52
47 56 39 48 05 18 13 26
21 02 29 10 63 40 55 32
59 44 51 36 17 06 25 14
20 03 28 11 62 41 54 33
58 45 50 37 16 07 24 15
030 compactcomplete
#[0,2,1,4,5,3]

00 23 08 31 44 59 36 51
45 58 37 50 01 22 09 30
02 21 10 29 46 57 38 49
47 56 39 48 03 20 11 28
19 04 27 12 63 40 55 32
62 41 54 33 18 05 26 13
17 06 25 14 61 42 53 34
60 43 52 35 16 07 24 15
031 compactcomplete
#[0,2,4,1,5,3]
_2[0,1,6,7,4,5,2,3]

00 23 08 31 44 59 36 51
45 58 37 50 01 22 09 30
03 20 11 28 47 56 39 48
46 57 38 49 02 21 10 29
19 04 27 12 63 40 55 32
62 41 54 33 18 05 26 13
16 07 24 15 60 43 52 35
61 42 53 34 17 06 25 14
032 compactcomplete
#[0,2,1,5,4,3]

00 23 08 31 44 59 36 51
46 57 38 49 02 21 10 29
01 22 09 30 45 58 37 50
47 56 39 48 03 20 11 28
19 04 27 12 63 40 55 32
61 42 53 34 17 06 25 14
18 05 26 13 62 41 54 33
60 43 52 35 16 07 24 15
033 compactcomplete
#[0,2,3,4,5,1]

00 23 08 31 56 47 48 39
57 46 49 38 01 22 09 30
02 21 10 29 58 45 50 37
59 44 51 36 03 20 11 28
07 16 15 24 63 40 55 32
62 41 54 33 06 17 14 25
05 18 13 26 61 42 53 34
60 43 52 35 04 19 12 27
034 compactcomplete
#[0,2,4,3,5,1]
_2[0,1,6,7,4,5,2,3]

00 23 08 31 56 47 48 39
57 46 49 38 01 22 09 30
03 20 11 28 59 44 51 36
58 45 50 37 02 21 10 29
07 16 15 24 63 40 55 32
62 41 54 33 06 17 14 25
04 19 12 27 60 43 52 35
61 42 53 34 05 18 13 26
035 compactcomplete
#[0,2,3,5,4,1]

00 23 08 31 56 47 48 39
58 45 50 37 02 21 10 29
01 22 09 30 57 46 49 38
59 44 51 36 03 20 11 28
07 16 15 24 63 40 55 32
61 42 53 34 05 18 13 26
06 17 14 25 62 41 54 33
60 43 52 35 04 19 12 27
036 compactcomplete
#[1,3,2,0,5,4]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 23 09 30 41 62 32 55
43 60 34 53 02 21 11 28
04 19 13 26 45 58 36 51
47 56 38 49 06 17 15 24
22 01 31 08 63 40 54 33
61 42 52 35 20 03 29 10
18 05 27 12 59 44 50 37
57 46 48 39 16 07 25 14
037 compactcomplete
#[2,0,3,1,4,5]
_3[0,1,6,7,4,5,2,3]

00 23 09 30 41 62 32 55
43 60 34 53 02 21 11 28
06 17 15 24 47 56 38 49
45 58 36 51 04 19 13 26
22 01 31 08 63 40 54 33
61 42 52 35 20 03 29 10
16 07 25 14 57 46 48 39
59 44 50 37 18 05 27 12
038 compactcomplete
#[1,4,2,0,5,3]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 23 09 30 41 62 32 55
45 58 36 51 04 19 13 26
02 21 11 28 43 60 34 53
47 56 38 49 06 17 15 24
22 01 31 08 63 40 54 33
59 44 50 37 18 05 27 12
20 03 29 10 61 42 52 35
57 46 48 39 16 07 25 14
039 compactcomplete
#[1,3,2,0,4,5]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 23 10 29 42 61 32 55
43 60 33 54 01 22 11 28
04 19 14 25 46 57 36 51
47 56 37 50 05 18 15 24
21 02 31 08 63 40 53 34
62 41 52 35 20 03 30 09
17 06 27 12 59 44 49 38
58 45 48 39 16 07 26 13
040 compactcomplete
#[2,0,3,1,5,4]
_3[0,1,6,7,4,5,2,3]

00 23 10 29 42 61 32 55
43 60 33 54 01 22 11 28
05 18 15 24 47 56 37 50
46 57 36 51 04 19 14 25
21 02 31 08 63 40 53 34
62 41 52 35 20 03 30 09
16 07 26 13 58 45 48 39
59 44 49 38 17 06 27 12
041 compactcomplete
#[1,5,2,0,4,3]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 23 10 29 42 61 32 55
46 57 36 51 04 19 14 25
01 22 11 28 43 60 33 54
47 56 37 50 05 18 15 24
21 02 31 08 63 40 53 34
59 44 49 38 17 06 27 12
20 03 30 09 62 41 52 35
58 45 48 39 16 07 26 13
042 compactcomplete
#[1,4,2,0,3,5]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 23 12 27 44 59 32 55
45 58 33 54 01 22 13 26
02 21 14 25 46 57 34 53
47 56 35 52 03 20 15 24
19 04 31 08 63 40 51 36
62 41 50 37 18 05 30 09
17 06 29 10 61 42 49 38
60 43 48 39 16 07 28 11
043 compactcomplete
#[2,0,4,1,5,3]
_3[0,1,6,7,4,5,2,3]

00 23 12 27 44 59 32 55
45 58 33 54 01 22 13 26
03 20 15 24 47 56 35 52
46 57 34 53 02 21 14 25
19 04 31 08 63 40 51 36
62 41 50 37 18 05 30 09
16 07 28 11 60 43 48 39
61 42 49 38 17 06 29 10
044 compactcomplete
#[1,5,2,0,3,4]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 23 12 27 44 59 32 55
46 57 34 53 02 21 14 25
01 22 13 26 45 58 33 54
47 56 35 52 03 20 15 24
19 04 31 08 63 40 51 36
61 42 49 38 17 06 29 10
18 05 30 09 62 41 50 37
60 43 48 39 16 07 28 11
045 compactcomplete
#[0,3,1,2,4,5]

00 27 04 31 37 62 33 58
39 60 35 56 02 25 06 29
08 19 12 23 45 54 41 50
47 52 43 48 10 17 14 21
26 01 30 05 63 36 59 32
61 38 57 34 24 03 28 07
18 09 22 13 55 44 51 40
53 46 49 42 16 11 20 15
046 compactcomplete
#[0,3,2,1,4,5]
_2[0,1,6,7,4,5,2,3]

00 27 04 31 37 62 33 58
39 60 35 56 02 25 06 29
10 17 14 21 47 52 43 48
45 54 41 50 08 19 12 23
26 01 30 05 63 36 59 32
61 38 57 34 24 03 28 07
16 11 20 15 53 46 49 42
55 44 51 40 18 09 22 13
047 compactcomplete
#[0,3,1,4,2,5]

00 27 04 31 37 62 33 58
45 54 41 50 08 19 12 23
02 25 06 29 39 60 35 56
47 52 43 48 10 17 14 21
26 01 30 05 63 36 59 32
55 44 51 40 18 09 22 13
24 03 28 07 61 38 57 34
53 46 49 42 16 11 20 15
048 compactcomplete
#[0,3,1,2,5,4]

00 27 04 31 38 61 34 57
39 60 35 56 01 26 05 30
08 19 12 23 46 53 42 49
47 52 43 48 09 18 13 22
25 02 29 06 63 36 59 32
62 37 58 33 24 03 28 07
17 10 21 14 55 44 51 40
54 45 50 41 16 11 20 15
049 compactcomplete
#[0,3,2,1,5,4]
_2[0,1,6,7,4,5,2,3]

00 27 04 31 38 61 34 57
39 60 35 56 01 26 05 30
09 18 13 22 47 52 43 48
46 53 42 49 08 19 12 23
25 02 29 06 63 36 59 32
62 37 58 33 24 03 28 07
16 11 20 15 54 45 50 41
55 44 51 40 17 10 21 14
050 compactcomplete
#[0,3,1,5,2,4]

00 27 04 31 38 61 34 57
46 53 42 49 08 19 12 23
01 26 05 30 39 60 35 56
47 52 43 48 09 18 13 22
25 02 29 06 63 36 59 32
55 44 51 40 17 10 21 14
24 03 28 07 62 37 58 33
54 45 50 41 16 11 20 15
051 compactcomplete
#[0,3,1,4,5,2]

00 27 04 31 44 55 40 51
45 54 41 50 01 26 05 30
02 25 06 29 46 53 42 49
47 52 43 48 03 24 07 28
19 08 23 12 63 36 59 32
62 37 58 33 18 09 22 13
17 10 21 14 61 38 57 34
60 39 56 35 16 11 20 15
052 compactcomplete
#[0,3,4,1,5,2]
_2[0,1,6,7,4,5,2,3]

00 27 04 31 44 55 40 51
45 54 41 50 01 26 05 30
03 24 07 28 47 52 43 48
46 53 42 49 02 25 06 29
19 08 23 12 63 36 59 32
62 37 58 33 18 09 22 13
16 11 20 15 60 39 56 35
61 38 57 34 17 10 21 14
053 compactcomplete
#[0,3,1,5,4,2]

00 27 04 31 44 55 40 51
46 53 42 49 02 25 06 29
01 26 05 30 45 54 41 50
47 52 43 48 03 24 07 28
19 08 23 12 63 36 59 32
61 38 57 34 17 10 21 14
18 09 22 13 62 37 58 33
60 39 56 35 16 11 20 15
054 compactcomplete
#[0,3,2,4,5,1]

00 27 04 31 52 47 48 43
53 46 49 42 01 26 05 30
02 25 06 29 54 45 50 41
55 44 51 40 03 24 07 28
11 16 15 20 63 36 59 32
62 37 58 33 10 17 14 21
09 18 13 22 61 38 57 34
60 39 56 35 08 19 12 23
055 compactcomplete
#[0,3,4,2,5,1]
_2[0,1,6,7,4,5,2,3]

00 27 04 31 52 47 48 43
53 46 49 42 01 26 05 30
03 24 07 28 55 44 51 40
54 45 50 41 02 25 06 29
11 16 15 20 63 36 59 32
62 37 58 33 10 17 14 21
08 19 12 23 60 39 56 35
61 38 57 34 09 18 13 22
056 compactcomplete
#[0,3,2,5,4,1]

00 27 04 31 52 47 48 43
54 45 50 41 02 25 06 29
01 26 05 30 53 46 49 42
55 44 51 40 03 24 07 28
11 16 15 20 63 36 59 32
61 38 57 34 09 18 13 22
10 17 14 21 62 37 58 33
60 39 56 35 08 19 12 23
057 compactcomplete
#[1,2,3,0,5,4]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 27 05 30 37 62 32 59
39 60 34 57 02 25 07 28
08 19 13 22 45 54 40 51
47 52 42 49 10 17 15 20
26 01 31 04 63 36 58 33
61 38 56 35 24 03 29 06
18 09 23 12 55 44 50 41
53 46 48 43 16 11 21 14
058 compactcomplete
#[2,1,3,0,5,4]
^[1,0]
_3[0,1,6,7,4,5,2,3]

00 27 05 30 37 62 32 59
39 60 34 57 02 25 07 28
10 17 15 20 47 52 42 49
45 54 40 51 08 19 13 22
26 01 31 04 63 36 58 33
61 38 56 35 24 03 29 06
16 11 21 14 53 46 48 43
55 44 50 41 18 09 23 12
059 compactcomplete
#[1,4,3,0,5,2]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 27 05 30 37 62 32 59
45 54 40 51 08 19 13 22
02 25 07 28 39 60 34 57
47 52 42 49 10 17 15 20
26 01 31 04 63 36 58 33
55 44 50 41 18 09 23 12
24 03 29 06 61 38 56 35
53 46 48 43 16 11 21 14
060 compactcomplete
#[1,2,3,0,4,5]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 27 06 29 38 61 32 59
39 60 33 58 01 26 07 28
08 19 14 21 46 53 40 51
47 52 41 50 09 18 15 20
25 02 31 04 63 36 57 34
62 37 56 35 24 03 30 05
17 10 23 12 55 44 49 42
54 45 48 43 16 11 22 13
061 compactcomplete
#[2,1,3,0,4,5]
^[1,0]
_3[0,1,6,7,4,5,2,3]

00 27 06 29 38 61 32 59
39 60 33 58 01 26 07 28
09 18 15 20 47 52 41 50
46 53 40 51 08 19 14 21
25 02 31 04 63 36 57 34
62 37 56 35 24 03 30 05
16 11 22 13 54 45 48 43
55 44 49 42 17 10 23 12
062 compactcomplete
#[1,5,3,0,4,2]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 27 06 29 38 61 32 59
46 53 40 51 08 19 14 21
01 26 07 28 39 60 33 58
47 52 41 50 09 18 15 20
25 02 31 04 63 36 57 34
55 44 49 42 17 10 23 12
24 03 30 05 62 37 56 35
54 45 48 43 16 11 22 13
063 compactcomplete
#[0,4,1,2,3,5]

00 29 02 31 35 62 33 60
39 58 37 56 04 25 06 27
08 21 10 23 43 54 41 52
47 50 45 48 12 17 14 19
28 01 30 03 63 34 61 32
59 38 57 36 24 05 26 07
20 09 22 11 55 42 53 40
51 46 49 44 16 13 18 15
064 compactcomplete
#[0,4,2,1,3,5]
_2[0,1,6,7,4,5,2,3]

00 29 02 31 35 62 33 60
39 58 37 56 04 25 06 27
12 17 14 19 47 50 45 48
43 54 41 52 08 21 10 23
28 01 30 03 63 34 61 32
59 38 57 36 24 05 26 07
16 13 18 15 51 46 49 44
55 42 53 40 20 09 22 11
065 compactcomplete
#[0,4,1,3,2,5]

00 29 02 31 35 62 33 60
43 54 41 52 08 21 10 23
04 25 06 27 39 58 37 56
47 50 45 48 12 17 14 19
28 01 30 03 63 34 61 32
55 42 53 40 20 09 22 11
24 05 26 07 59 38 57 36
51 46 49 44 16 13 18 15
066 compactcomplete
#[0,4,1,2,5,3]

00 29 02 31 38 59 36 57
39 58 37 56 01 28 03 30
08 21 10 23 46 51 44 49
47 50 45 48 09 20 11 22
25 04 27 06 63 34 61 32
62 35 60 33 24 05 26 07
17 12 19 14 55 42 53 40
54 43 52 41 16 13 18 15
067 compactcomplete
#[0,4,2,1,5,3]
_2[0,1,6,7,4,5,2,3]

00 29 02 31 38 59 36 57
39 58 37 56 01 28 03 30
09 20 11 22 47 50 45 48
46 51 44 49 08 21 10 23
25 04 27 06 63 34 61 32
62 35 60 33 24 05 26 07
16 13 18 15 54 43 52 41
55 42 53 40 17 12 19 14
068 compactcomplete
#[0,4,1,5,2,3]

00 29 02 31 38 59 36 57
46 51 44 49 08 21 10 23
01 28 03 30 39 58 37 56
47 50 45 48 09 20 11 22
25 04 27 06 63 34 61 32
55 42 53 40 17 12 19 14
24 05 26 07 62 35 60 33
54 43 52 41 16 13 18 15
069 compactcomplete
#[0,4,1,3,5,2]

00 29 02 31 42 55 40 53
43 54 41 52 01 28 03 30
04 25 06 27 46 51 44 49
47 50 45 48 05 24 07 26
21 08 23 10 63 34 61 32
62 35 60 33 20 09 22 11
17 12 19 14 59 38 57 36
58 39 56 37 16 13 18 15
070 compactcomplete
#[0,4,3,1,5,2]
_2[0,1,6,7,4,5,2,3]

00 29 02 31 42 55 40 53
43 54 41 52 01 28 03 30
05 24 07 26 47 50 45 48
46 51 44 49 04 25 06 27
21 08 23 10 63 34 61 32
62 35 60 33 20 09 22 11
16 13 18 15 58 39 56 37
59 38 57 36 17 12 19 14
071 compactcomplete
#[0,4,1,5,3,2]

00 29 02 31 42 55 40 53
46 51 44 49 04 25 06 27
01 28 03 30 43 54 41 52
47 50 45 48 05 24 07 26
21 08 23 10 63 34 61 32
59 38 57 36 17 12 19 14
20 09 22 11 62 35 60 33
58 39 56 37 16 13 18 15
072 compactcomplete
#[0,4,2,3,5,1]

00 29 02 31 50 47 48 45
51 46 49 44 01 28 03 30
04 25 06 27 54 43 52 41
55 42 53 40 05 24 07 26
13 16 15 18 63 34 61 32
62 35 60 33 12 17 14 19
09 20 11 22 59 38 57 36
58 39 56 37 08 21 10 23
073 compactcomplete
#[0,4,3,2,5,1]
_2[0,1,6,7,4,5,2,3]

00 29 02 31 50 47 48 45
51 46 49 44 01 28 03 30
05 24 07 26 55 42 53 40
54 43 52 41 04 25 06 27
13 16 15 18 63 34 61 32
62 35 60 33 12 17 14 19
08 21 10 23 58 39 56 37
59 38 57 36 09 20 11 22
074 compactcomplete
#[0,4,2,5,3,1]

00 29 02 31 50 47 48 45
54 43 52 41 04 25 06 27
01 28 03 30 51 46 49 44
55 42 53 40 05 24 07 26
13 16 15 18 63 34 61 32
59 38 57 36 09 20 11 22
12 17 14 19 62 35 60 33
58 39 56 37 08 21 10 23
075 compactcomplete
#[1,2,4,0,5,3]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 29 03 30 35 62 32 61
39 58 36 57 04 25 07 26
08 21 11 22 43 54 40 53
47 50 44 49 12 17 15 18
28 01 31 02 63 34 60 33
59 38 56 37 24 05 27 06
20 09 23 10 55 42 52 41
51 46 48 45 16 13 19 14
076 compactcomplete
#[2,1,4,0,5,3]
^[1,0]
_3[0,1,6,7,4,5,2,3]

00 29 03 30 35 62 32 61
39 58 36 57 04 25 07 26
12 17 15 18 47 50 44 49
43 54 40 53 08 21 11 22
28 01 31 02 63 34 60 33
59 38 56 37 24 05 27 06
16 13 19 14 51 46 48 45
55 42 52 41 20 09 23 10
077 compactcomplete
#[1,3,4,0,5,2]
^[1,0]
_1[0,1,6,7,4,5,2,3]

00 29 03 30 35 62 32 61
43 54 40 53 08 21 11 22
04 25 07 26 39 58 36 57
47 50 44 49 12 17 15 18
28 01 31 02 63 34 60 33
55 42 52 41 20 09 23 10
24 05 27 06 59 38 56 37
51 46 48 45 16 13 19 14
078 compactcomplete
#[0,5,1,2,3,4]

00 30 01 31 35 61 34 60
39 57 38 56 04 26 05 27
08 22 09 23 43 53 42 52
47 49 46 48 12 18 13 19
28 02 29 03 63 33 62 32
59 37 58 36 24 06 25 07
20 10 21 11 55 41 54 40
51 45 50 44 16 14 17 15
079 compactcomplete
#[0,5,2,1,3,4]
_2[0,1,6,7,4,5,2,3]

00 30 01 31 35 61 34 60
39 57 38 56 04 26 05 27
12 18 13 19 47 49 46 48
43 53 42 52 08 22 09 23
28 02 29 03 63 33 62 32
59 37 58 36 24 06 25 07
16 14 17 15 51 45 50 44
55 41 54 40 20 10 21 11
080 compactcomplete
#[0,5,1,3,2,4]

00 30 01 31 35 61 34 60
43 53 42 52 08 22 09 23
04 26 05 27 39 57 38 56
47 49 46 48 12 18 13 19
28 02 29 03 63 33 62 32
55 41 54 40 20 10 21 11
24 06 25 07 59 37 58 36
51 45 50 44 16 14 17 15
081 compactcomplete
#[0,5,1,2,4,3]

00 30 01 31 37 59 36 58
39 57 38 56 02 28 03 29
08 22 09 23 45 51 44 50
47 49 46 48 10 20 11 21
26 04 27 05 63 33 62 32
61 35 60 34 24 06 25 07
18 12 19 13 55 41 54 40
53 43 52 42 16 14 17 15
082 compactcomplete
#[0,5,2,1,4,3]
_2[0,1,6,7,4,5,2,3]

00 30 01 31 37 59 36 58
39 57 38 56 02 28 03 29
10 20 11 21 47 49 46 48
45 51 44 50 08 22 09 23
26 04 27 05 63 33 62 32
61 35 60 34 24 06 25 07
16 14 17 15 53 43 52 42
55 41 54 40 18 12 19 13
083 compactcomplete
#[0,5,1,4,2,3]

00 30 01 31 37 59 36 58
45 51 44 50 08 22 09 23
02 28 03 29 39 57 38 56
47 49 46 48 10 20 11 21
26 04 27 05 63 33 62 32
55 41 54 40 18 12 19 13
24 06 25 07 61 35 60 34
53 43 52 42 16 14 17 15
084 compactcomplete
#[0,5,1,3,4,2]

00 30 01 31 41 55 40 54
43 53 42 52 02 28 03 29
04 26 05 27 45 51 44 50
47 49 46 48 06 24 07 25
22 08 23 09 63 33 62 32
61 35 60 34 20 10 21 11
18 12 19 13 59 37 58 36
57 39 56 38 16 14 17 15
085 compactcomplete
#[0,5,3,1,4,2]
_2[0,1,6,7,4,5,2,3]

00 30 01 31 41 55 40 54
43 53 42 52 02 28 03 29
06 24 07 25 47 49 46 48
45 51 44 50 04 26 05 27
22 08 23 09 63 33 62 32
61 35 60 34 20 10 21 11
16 14 17 15 57 39 56 38
59 37 58 36 18 12 19 13
086 compactcomplete
#[0,5,1,4,3,2]

00 30 01 31 41 55 40 54
45 51 44 50 04 26 05 27
02 28 03 29 43 53 42 52
47 49 46 48 06 24 07 25
22 08 23 09 63 33 62 32
59 37 58 36 18 12 19 13
20 10 21 11 61 35 60 34
57 39 56 38 16 14 17 15
087 compactcomplete
#[0,5,2,3,4,1]

00 30 01 31 49 47 48 46
51 45 50 44 02 28 03 29
04 26 05 27 53 43 52 42
55 41 54 40 06 24 07 25
14 16 15 17 63 33 62 32
61 35 60 34 12 18 13 19
10 20 11 21 59 37 58 36
57 39 56 38 08 22 09 23
088 compactcomplete
#[0,5,3,2,4,1]
_2[0,1,6,7,4,5,2,3]

00 30 01 31 49 47 48 46
51 45 50 44 02 28 03 29
06 24 07 25 55 41 54 40
53 43 52 42 04 26 05 27
14 16 15 17 63 33 62 32
61 35 60 34 12 18 13 19
08 22 09 23 57 39 56 38
59 37 58 36 10 20 11 21
089 compactcomplete
#[0,5,2,4,3,1]

00 30 01 31 49 47 48 46
53 43 52 42 04 26 05 27
02 28 03 29 51 45 50 44
55 41 54 40 06 24 07 25
14 16 15 17 63 33 62 32
59 37 58 36 10 20 11 21
12 18 13 19 61 35 60 34
57 39 56 38 08 22 09 23