logo
Octamatch   Index  |  Home  |  Send Your Feedback
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 H47: 1 of 1654idem
0,2,945: 1 of 54248: 3 of 1658
0,2,10 D56: 4 of 4138 / 2 50: 6 of 7390 / 2
0,2,1147: 2 of 544147: 7 of 6748
0,2,1344: 4 of 882346: 7 of 9066
0,2,1447: 2 of 255053: 12 of 8638
0,2,1548: 1 of 63848: 5 of 1929
0,2,1641: 1 of 6641: 7 of 171
0,2,1747: 1 of 496746: 7 of 6028
0,2,1844: 7 of 65742: 1 of 158
0,2,1947: 2 of 120247: 2 of 848
0,2,2043: 5 of 36147: 1 of 2234
0,2,2143: 1 of 51848: 2 of 2095
0,2,2252: 1 of 501852: 4 of 6747
0,2,2348: 1 of 118744: 11 of 557
0,2,2447: 1 of 128145: 36 of 196
0,3,639: 2 of 55--
0,3,9--46: 4 of 285
0,3,1148: 2 of 79944: 2 of 720
0,3,1346: 1 of 98346: 1 of 1051
0,3,1445: 1 of 77345: 4 of 562
0,3,15 D54: 1 of 30 / 2 49: 4 of 120 / 2
0,3,1636: 2 of 4641: 1 of 27
0,3,1748: 2 of 80746: 1 of 1035
0,3,1834: 3 of 1939: 2 of 34
0,3,1945: 3 of 11946: 1 of 37
0,3,2044: 1 of 3544: 3 of 199
0,3,2147: 1 of 4047: 4 of 55
0,3,2247: 1 of 65845: 2 of 583
0,3,2345: 2 of 10346: 1 of 34
0,3,2448: 6 of 14447: 1 of 50
0,4,635: 2 of 39--
0,4,7 H46: 3 of 746idem
0,4,1145: 2 of 66346: 3 of 984
0,4,1642: 9 of 4841: 3 of 79
0,4,17 H47: 1 of 904idem
0,4,20 D46: 4 of 84 / 2 49: 4 of 222 / 2
0,4,2147: 1 of 4744: 1 of 100
0,4,22 H43: 2 of 540idem
0,6,840: 1 of 19--
0,6,934: 1 of 5--
0,6,1347: 2 of 671--
0,6,1446: 2 of 665--
0,6,1942: 6 of 192--
0,6,24 D39: 1 of 232 / 2 --
0,7,945: 1 of 75045: 1 of 928
0,7,11 D56: 2 of 6734 / 2 --
0,7,13--54: 10 of 3053
0,7,1446: 3 of 840144: 19 of 2818
0,7,1644: 1 of 19245: 1 of 183
0,7,1752: 1 of 552751: 2 of 2628
0,7,1843: 6 of 85940: 2 of 128
0,7,1945: 1 of 152747: 2 of 340
0,7,2148: 2 of 55546: 1 of 502
0,7,2246: 4 of 475145: 2 of 2221
0,7,2346: 3 of 159445: 2 of 356
0,7,2450: 2 of 186739: 3 of 132
0,8,1744: 1 of 25538: 1 of 130
0,8,1836: 1 of 18--
0,8,1945: 1 of 46--
0,8,2132: 1 of 1241: 1 of 20
0,8,2243: 2 of 15142: 2 of 56
0,8,2339: 3 of 27--
0,8,24 D42: 1 of 60 / 2 --
0,9,1748: 2 of 75143: 1 of 489
0,9,1845: 2 of 6138: 2 of 5
0,9,1945: 5 of 16935: 2 of 19
0,9,21 D42: 1 of 28 / 2 42: 1 of 20 / 2
0,9,2246: 3 of 50644: 4 of 298
0,9,2345: 3 of 9537: 1 of 40
0,13,17 D56: 4 of 7690 / 2 --
0,13,2249: 1 of 711346: 13 of 2280
0,13,2348: 3 of 209443: 2 of 319
0,14,22 D55: 4 of 6184 / 2 52: 4 of 958 / 2
0,14,2352: 1 of 170735: 1 of 50
0,19,23 D55: 2 of 808 / 2 --
1,3,549: 1 of 614--
1,3,1045: 3 of 109742: 2 of 769
1,3,1147: 1 of 152445: 4 of 2176
1,3,1540: 1 of 2543: 1 of 70
1,3,1637: 1 of 1549: 1 of 6
1,3,17 H47: 1 of 1185idem
1,3,2148: 1 of 6749: 4 of 109
1,3,22 H44: 12 of 856idem
1,5,842: 2 of 59--
1,5,949: 1 of 660--
1,5,1351: 1 of 3504--
1,5,1452: 6 of 2842--
1,5,18 D53: 2 of 698 / 2 --
1,5,1951: 1 of 846--
1,8,1042: 2 of 18240: 7 of 248
1,8,1142: 6 of 19845: 3 of 696
1,8,1535: 1 of 1747: 2 of 83
1,8,1739: 4 of 17638: 6 of 209
1,8,1840: 1 of 832: 2 of 3
1,8,19 D40: 1 of 60 / 2 --
1,8,2135: 1 of 2747: 2 of 31
1,8,2241: 4 of 10338: 3 of 86
1,8,2334: 1 of 2--
1,9,1044: 6 of 95743: 2 of 455
1,9,1147: 1 of 113941: 4 of 365
1,9,1538: 2 of 2649: 4 of 106
1,9,16--49: 1 of 6
1,9,1748: 1 of 92845: 3 of 458
1,9,2138: 2 of 3243: 1 of 33
1,9,2247: 2 of 85640: 6 of 336
1,10,1347: 1 of 549042: 7 of 1125
1,10,1452: 2 of 713753: 6 of 1851
1,10,1745: 1 of 1041946: 3 of 2055
1,10,1849: 3 of 1356--
1,10,1947: 3 of 155640: 3 of 98
1,10,21 V42: 8 of 827idem
1,10,2246: 1 of 356850: 2 of 1548
1,10,2348: 2 of 211935: 4 of 98
1,11,1352: 1 of 669649: 1 of 1542
1,11,1445: 2 of 637943: 3 of 1250
1,11,17--51: 12 of 6965
1,11,1852: 1 of 1295--
1,11,1945: 2 of 212845: 2 of 209
1,11,21 V47: 1 of 1171idem
1,11,2245: 4 of 1138745: 12 of 4634
1,11,2350: 3 of 193739: 9 of 154
1,13,1642: 6 of 14140: 1 of 34
1,13,1751: 2 of 5586--
1,13,21 V40: 6 of 270idem
1,13,2246: 1 of 728745: 1 of 2592
1,14,1640: 3 of 11434: 6 of 22
1,14,1745: 2 of 716244: 2 of 1517
1,14,21 V47: 2 of 362idem
1,14,2251: 4 of 647145: 4 of 418
1,16,1840: 1 of 2--
1,16,1934: 4 of 4--
2,10,1354: 2 of 3401047: 6 of 10151
2,10,14 H49: 7 of 11255idem
2,10,1853: 4 of 3938--
2,11,13 H49: 2 of 32023idem
2,11,17--50: 1 of 32958
2,11,1843: 7 of 352847: 2 of 747
2,11,22 V50: 22 of 31002idem
2,16,18 H34: 1 of 12idem
6,8,17 H38: 1 of 5idem
6,13,17 D53: 1 of 1332 / 2 --
472145 = 321674 + 150471