There are 4,845,739 groups of squares with center 13. The biggest group has 228,960 squares. The 3,884,052 smallest groups have 2 squares each.
There are 452 group sizes.
Group Size | Number of Groups | Group Size | Number of Groups | Group Size | Number of Groups | Group Size | Number of Groups | Group Size | Number of Groups | Group Size | Number of Groups |
---|---|---|---|---|---|---|---|---|---|---|---|
228960 | 1 | 1608 | 6 | 864 | 8 | 532 | 2 | 312 | 36 | 144 | 109 |
174240 | 2 | 1592 | 2 | 852 | 4 | 528 | 23 | 310 | 8 | 142 | 32 |
145632 | 2 | 1584 | 2 | 848 | 10 | 526 | 4 | 308 | 10 | 140 | 76 |
90144 | 1 | 1576 | 2 | 844 | 4 | 524 | 2 | 306 | 4 | 138 | 44 |
48544 | 3 | 1548 | 2 | 840 | 14 | 520 | 12 | 304 | 38 | 136 | 172 |
45072 | 2 | 1536 | 2 | 836 | 8 | 518 | 20 | 302 | 4 | 134 | 36 |
43776 | 1 | 1532 | 4 | 832 | 8 | 516 | 10 | 300 | 16 | 132 | 92 |
22536 | 4 | 1520 | 4 | 828 | 4 | 512 | 4 | 298 | 4 | 130 | 12 |
18784 | 2 | 1512 | 4 | 826 | 8 | 508 | 6 | 296 | 22 | 128 | 178 |
16896 | 2 | 1508 | 4 | 808 | 4 | 506 | 8 | 292 | 24 | 126 | 24 |
12544 | 2 | 1474 | 4 | 804 | 4 | 504 | 6 | 288 | 28 | 124 | 94 |
12192 | 2 | 1468 | 4 | 800 | 16 | 500 | 14 | 286 | 4 | 122 | 28 |
11568 | 2 | 1456 | 4 | 796 | 4 | 496 | 6 | 284 | 18 | 120 | 172 |
10848 | 2 | 1446 | 4 | 792 | 14 | 492 | 8 | 282 | 4 | 118 | 28 |
10272 | 2 | 1432 | 4 | 784 | 4 | 490 | 12 | 280 | 24 | 116 | 154 |
9004 | 2 | 1426 | 8 | 780 | 4 | 488 | 19 | 278 | 8 | 114 | 20 |
8352 | 2 | 1424 | 2 | 776 | 8 | 484 | 6 | 276 | 16 | 112 | 220 |
7008 | 2 | 1400 | 8 | 772 | 4 | 482 | 4 | 272 | 36 | 110 | 64 |
6656 | 2 | 1368 | 4 | 770 | 4 | 480 | 18 | 268 | 26 | 108 | 154 |
6456 | 4 | 1352 | 6 | 768 | 4 | 476 | 12 | 264 | 32 | 106 | 80 |
6432 | 2 | 1344 | 4 | 762 | 4 | 472 | 26 | 262 | 8 | 104 | 208 |
6400 | 2 | 1336 | 4 | 760 | 6 | 468 | 2 | 260 | 28 | 102 | 76 |
6272 | 1 | 1328 | 4 | 756 | 4 | 464 | 16 | 258 | 4 | 100 | 290 |
6096 | 1 | 1312 | 2 | 752 | 14 | 460 | 10 | 256 | 45 | 98 | 104 |
5936 | 6 | 1296 | 8 | 750 | 8 | 456 | 18 | 254 | 4 | 96 | 359 |
5536 | 2 | 1294 | 8 | 744 | 14 | 454 | 4 | 252 | 30 | 94 | 48 |
5264 | 4 | 1288 | 18 | 736 | 8 | 452 | 10 | 250 | 4 | 92 | 230 |
5088 | 2 | 1276 | 4 | 728 | 4 | 448 | 52 | 248 | 30 | 90 | 120 |
4992 | 4 | 1272 | 4 | 724 | 8 | 444 | 10 | 244 | 14 | 88 | 322 |
4904 | 2 | 1256 | 4 | 722 | 4 | 440 | 6 | 240 | 48 | 86 | 100 |
4376 | 2 | 1248 | 2 | 720 | 8 | 436 | 8 | 238 | 4 | 84 | 252 |
4320 | 2 | 1240 | 8 | 716 | 4 | 432 | 14 | 236 | 12 | 82 | 120 |
4256 | 7 | 1232 | 2 | 712 | 10 | 430 | 4 | 234 | 8 | 80 | 538 |
4224 | 4 | 1224 | 4 | 708 | 4 | 428 | 2 | 232 | 44 | 78 | 164 |
4104 | 2 | 1216 | 10 | 704 | 6 | 424 | 24 | 230 | 16 | 76 | 408 |
4096 | 2 | 1212 | 4 | 700 | 4 | 420 | 16 | 228 | 18 | 74 | 176 |
4048 | 2 | 1204 | 4 | 692 | 8 | 416 | 20 | 226 | 28 | 72 | 607 |
3312 | 2 | 1156 | 4 | 688 | 8 | 412 | 8 | 224 | 86 | 70 | 256 |
3216 | 4 | 1136 | 4 | 684 | 4 | 410 | 12 | 222 | 12 | 68 | 418 |
3120 | 2 | 1132 | 2 | 680 | 4 | 408 | 8 | 220 | 42 | 66 | 248 |
3068 | 4 | 1128 | 4 | 676 | 16 | 404 | 18 | 218 | 4 | 64 | 1032 |
3064 | 2 | 1124 | 2 | 672 | 14 | 402 | 4 | 216 | 46 | 62 | 268 |
2928 | 4 | 1100 | 10 | 668 | 4 | 400 | 10 | 214 | 12 | 60 | 742 |
2844 | 4 | 1096 | 4 | 664 | 8 | 392 | 4 | 212 | 28 | 58 | 308 |
2736 | 4 | 1084 | 6 | 656 | 9 | 390 | 4 | 210 | 8 | 56 | 1094 |
2728 | 4 | 1068 | 8 | 648 | 8 | 386 | 4 | 208 | 53 | 54 | 420 |
2672 | 6 | 1064 | 2 | 640 | 2 | 384 | 16 | 206 | 16 | 52 | 910 |
2640 | 4 | 1056 | 3 | 636 | 6 | 382 | 4 | 204 | 86 | 50 | 576 |
2596 | 6 | 1040 | 10 | 632 | 4 | 380 | 2 | 202 | 20 | 48 | 1505 |
2592 | 2 | 1032 | 2 | 628 | 4 | 378 | 4 | 200 | 74 | 46 | 552 |
2576 | 4 | 1024 | 6 | 624 | 8 | 376 | 34 | 198 | 4 | 44 | 1364 |
2432 | 12 | 1020 | 4 | 620 | 8 | 374 | 4 | 196 | 28 | 42 | 756 |
2336 | 4 | 1016 | 4 | 616 | 18 | 372 | 12 | 194 | 4 | 40 | 2350 |
2172 | 4 | 1008 | 4 | 608 | 6 | 370 | 4 | 192 | 104 | 38 | 984 |
2160 | 4 | 1004 | 4 | 604 | 8 | 368 | 6 | 190 | 4 | 36 | 2476 |
2136 | 4 | 1000 | 4 | 600 | 16 | 364 | 20 | 188 | 32 | 34 | 1232 |
2092 | 6 | 998 | 4 | 596 | 8 | 360 | 18 | 186 | 12 | 32 | 4326 |
2080 | 8 | 992 | 4 | 592 | 12 | 358 | 4 | 184 | 70 | 30 | 1780 |
2064 | 2 | 988 | 4 | 588 | 4 | 356 | 16 | 182 | 12 | 28 | 4006 |
2016 | 4 | 980 | 16 | 584 | 6 | 354 | 4 | 180 | 18 | 26 | 2688 |
1960 | 5 | 972 | 4 | 580 | 6 | 352 | 34 | 178 | 12 | 24 | 7314 |
1952 | 6 | 960 | 2 | 578 | 4 | 348 | 12 | 176 | 98 | 22 | 3936 |
1944 | 1 | 952 | 6 | 576 | 22 | 346 | 16 | 174 | 24 | 20 | 10026 |
1936 | 6 | 944 | 4 | 572 | 4 | 344 | 32 | 172 | 16 | 18 | 6524 |
1920 | 2 | 936 | 4 | 570 | 4 | 342 | 4 | 170 | 8 | 16 | 21628 |
1856 | 5 | 928 | 14 | 566 | 4 | 340 | 18 | 168 | 112 | 14 | 11300 |
1848 | 4 | 916 | 4 | 564 | 8 | 336 | 14 | 166 | 8 | 12 | 26800 |
1800 | 4 | 912 | 4 | 560 | 6 | 334 | 4 | 164 | 40 | 10 | 31412 |
1776 | 2 | 904 | 4 | 556 | 4 | 332 | 6 | 162 | 28 | 8 | 140558 |
1760 | 2 | 900 | 4 | 552 | 4 | 330 | 12 | 160 | 82 | 6 | 82972 |
1736 | 2 | 896 | 17 | 550 | 4 | 328 | 16 | 158 | 40 | 4 | 578644 |
1728 | 2 | 892 | 4 | 548 | 12 | 326 | 4 | 156 | 56 | 2 | 3884052 |
1696 | 18 | 888 | 6 | 544 | 20 | 324 | 24 | 154 | 24 | - | - |
1664 | 4 | 880 | 7 | 542 | 4 | 322 | 4 | 152 | 134 | - | - |
1628 | 4 | 876 | 8 | 540 | 8 | 320 | 37 | 148 | 70 | - | - |
1616 | 4 | 872 | 4 | 536 | 6 | 316 | 24 | 146 | 12 | - | - |
Note 1: For terms used below see Terms.
Note 2: Group numbers refer to all the groups, not just those with center 13.
These are symborder squares. The associative squares, (group 7 below), and those of 9 other groups are also symborder.
The number of squares in the group is shown below each group number.
Group 1: concentric, symlateral hybrid
Group 2: concentric
Group 3: symlateral
Group 4: associative, concentric hybrid
Group 5: associative, symlateral hybrid
Order5Special makes the concentric squares.
Groups 6, 10, 11 (below): middle row/column are symmetric;
main diagonal pairs are adjacent, interleaved
Group 10: opposite paired
Group 11: side paired
Group 6: hybrid of groups 10, 11
with twice as many squares
Group 7: associative
Group 8: octant boundary pairs are interleaved
Group 9: octant boundary pairs are adjacent
Order5Special makes the associative squares.
Group 10 combines characteristics of groups 17 and 19 with twice as many squares.
Group 11 combines characteristics of groups 18 and 20 with twice as many squares.