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This page shows possible placements of the solids with 4 squares on two opposite corners and the rest diamonds.

The total number of solutions is nearly half a million.
Contrast this pattern with corners2.html, which has just 3 squares in each corner and 2552 solutions TOTAL!

At the bottom of the page, some example solutions are shown, those with more than 85% symmetry.

This table shows how many solutions exist for each position of the solids, the maximum degree of symmetry (out of 60), and how many of the solutions have the highest symmetry.
(Where the solids are diagonally symmetric (D), each basic solution is found twice; where the solids are horizontally or vertically symmetric (H or V), the same solutions are found for each set or corners.)

 0,2,4 H 47: 1 of 1654 idem 0,2,9 45: 1 of 542 48: 3 of 1658 0,2,10 D 56: 4 of 4138 / 2 50: 6 of 7390 / 2 0,2,11 47: 2 of 5441 47: 7 of 6748 0,2,13 44: 4 of 8823 46: 7 of 9066 0,2,14 47: 2 of 2550 53: 12 of 8638 0,2,15 48: 1 of 638 48: 5 of 1929 0,2,16 41: 1 of 66 41: 7 of 171 0,2,17 47: 1 of 4967 46: 7 of 6028 0,2,18 44: 7 of 657 42: 1 of 158 0,2,19 47: 2 of 1202 47: 2 of 848 0,2,20 43: 5 of 361 47: 1 of 2234 0,2,21 43: 1 of 518 48: 2 of 2095 0,2,22 52: 1 of 5018 52: 4 of 6747 0,2,23 48: 1 of 1187 44: 11 of 557 0,2,24 47: 1 of 1281 45: 36 of 196 0,3,6 39: 2 of 55 -- 0,3,9 -- 46: 4 of 285 0,3,11 48: 2 of 799 44: 2 of 720 0,3,13 46: 1 of 983 46: 1 of 1051 0,3,14 45: 1 of 773 45: 4 of 562 0,3,15 D 54: 1 of 30 / 2 49: 4 of 120 / 2 0,3,16 36: 2 of 46 41: 1 of 27 0,3,17 48: 2 of 807 46: 1 of 1035 0,3,18 34: 3 of 19 39: 2 of 34 0,3,19 45: 3 of 119 46: 1 of 37 0,3,20 44: 1 of 35 44: 3 of 199 0,3,21 47: 1 of 40 47: 4 of 55 0,3,22 47: 1 of 658 45: 2 of 583 0,3,23 45: 2 of 103 46: 1 of 34 0,3,24 48: 6 of 144 47: 1 of 50 0,4,6 35: 2 of 39 -- 0,4,7 H 46: 3 of 746 idem 0,4,11 45: 2 of 663 46: 3 of 984 0,4,16 42: 9 of 48 41: 3 of 79 0,4,17 H 47: 1 of 904 idem 0,4,20 D 46: 4 of 84 / 2 49: 4 of 222 / 2 0,4,21 47: 1 of 47 44: 1 of 100 0,4,22 H 43: 2 of 540 idem 0,6,8 40: 1 of 19 -- 0,6,9 34: 1 of 5 -- 0,6,13 47: 2 of 671 -- 0,6,14 46: 2 of 665 -- 0,6,19 42: 6 of 192 -- 0,6,24 D 39: 1 of 232 / 2 -- 0,7,9 45: 1 of 750 45: 1 of 928 0,7,11 D 56: 2 of 6734 / 2 -- 0,7,13 -- 54: 10 of 3053
 0,7,14 46: 3 of 8401 44: 19 of 2818 0,7,16 44: 1 of 192 45: 1 of 183 0,7,17 52: 1 of 5527 51: 2 of 2628 0,7,18 43: 6 of 859 40: 2 of 128 0,7,19 45: 1 of 1527 47: 2 of 340 0,7,21 48: 2 of 555 46: 1 of 502 0,7,22 46: 4 of 4751 45: 2 of 2221 0,7,23 46: 3 of 1594 45: 2 of 356 0,7,24 50: 2 of 1867 39: 3 of 132 0,8,17 44: 1 of 255 38: 1 of 130 0,8,18 36: 1 of 18 -- 0,8,19 45: 1 of 46 -- 0,8,21 32: 1 of 12 41: 1 of 20 0,8,22 43: 2 of 151 42: 2 of 56 0,8,23 39: 3 of 27 -- 0,8,24 D 42: 1 of 60 / 2 -- 0,9,17 48: 2 of 751 43: 1 of 489 0,9,18 45: 2 of 61 38: 2 of 5 0,9,19 45: 5 of 169 35: 2 of 19 0,9,21 D 42: 1 of 28 / 2 42: 1 of 20 / 2 0,9,22 46: 3 of 506 44: 4 of 298 0,9,23 45: 3 of 95 37: 1 of 40 0,13,17 D 56: 4 of 7690 / 2 -- 0,13,22 49: 1 of 7113 46: 13 of 2280 0,13,23 48: 3 of 2094 43: 2 of 319 0,14,22 D 55: 4 of 6184 / 2 52: 4 of 958 / 2 0,14,23 52: 1 of 1707 35: 1 of 50 0,19,23 D 55: 2 of 808 / 2 -- 1,3,5 49: 1 of 614 -- 1,3,10 45: 3 of 1097 42: 2 of 769 1,3,11 47: 1 of 1524 45: 4 of 2176 1,3,15 40: 1 of 25 43: 1 of 70 1,3,16 37: 1 of 15 49: 1 of 6 1,3,17 H 47: 1 of 1185 idem 1,3,21 48: 1 of 67 49: 4 of 109 1,3,22 H 44: 12 of 856 idem 1,5,8 42: 2 of 59 -- 1,5,9 49: 1 of 660 -- 1,5,13 51: 1 of 3504 -- 1,5,14 52: 6 of 2842 -- 1,5,18 D 53: 2 of 698 / 2 -- 1,5,19 51: 1 of 846 -- 1,8,10 42: 2 of 182 40: 7 of 248 1,8,11 42: 6 of 198 45: 3 of 696 1,8,15 35: 1 of 17 47: 2 of 83 1,8,17 39: 4 of 176 38: 6 of 209 1,8,18 40: 1 of 8 32: 2 of 3 1,8,19 D 40: 1 of 60 / 2 --
 1,8,21 35: 1 of 27 47: 2 of 31 1,8,22 41: 4 of 103 38: 3 of 86 1,8,23 34: 1 of 2 -- 1,9,10 44: 6 of 957 43: 2 of 455 1,9,11 47: 1 of 1139 41: 4 of 365 1,9,15 38: 2 of 26 49: 4 of 106 1,9,16 -- 49: 1 of 6 1,9,17 48: 1 of 928 45: 3 of 458 1,9,21 38: 2 of 32 43: 1 of 33 1,9,22 47: 2 of 856 40: 6 of 336 1,10,13 47: 1 of 5490 42: 7 of 1125 1,10,14 52: 2 of 7137 53: 6 of 1851 1,10,17 45: 1 of 10419 46: 3 of 2055 1,10,18 49: 3 of 1356 -- 1,10,19 47: 3 of 1556 40: 3 of 98 1,10,21 V 42: 8 of 827 idem 1,10,22 46: 1 of 3568 50: 2 of 1548 1,10,23 48: 2 of 2119 35: 4 of 98 1,11,13 52: 1 of 6696 49: 1 of 1542 1,11,14 45: 2 of 6379 43: 3 of 1250 1,11,17 -- 51: 12 of 6965 1,11,18 52: 1 of 1295 -- 1,11,19 45: 2 of 2128 45: 2 of 209 1,11,21 V 47: 1 of 1171 idem 1,11,22 45: 4 of 11387 45: 12 of 4634 1,11,23 50: 3 of 1937 39: 9 of 154 1,13,16 42: 6 of 141 40: 1 of 34 1,13,17 51: 2 of 5586 -- 1,13,21 V 40: 6 of 270 idem 1,13,22 46: 1 of 7287 45: 1 of 2592 1,14,16 40: 3 of 114 34: 6 of 22 1,14,17 45: 2 of 7162 44: 2 of 1517 1,14,21 V 47: 2 of 362 idem 1,14,22 51: 4 of 6471 45: 4 of 418 1,16,18 40: 1 of 2 -- 1,16,19 34: 4 of 4 -- 2,10,13 54: 2 of 34010 47: 6 of 10151 2,10,14 H 49: 7 of 11255 idem 2,10,18 53: 4 of 3938 -- 2,11,13 H 49: 2 of 32023 idem 2,11,17 -- 50: 1 of 32958 2,11,18 43: 7 of 3528 47: 2 of 747 2,11,22 V 50: 22 of 31002 idem 2,16,18 H 34: 1 of 12 idem 6,8,17 H 38: 1 of 5 idem 6,13,17 D 53: 1 of 1332 / 2 -- 472145 = 321674 + 150471