Square, n = 34 record
A = 0.004834891576935…
full precision
Exact value of the published coordinate literals:
0.00483489157693571405689096340347
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
62 triangles tied (within relative 10−9) at the minimal area, in 62 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0657 · 0.1954 · 0.2436 |
(17,22,25) |
| 1 | 0.0661 · 0.1951 · 0.2439 |
(19,28,30) |
| 1 | 0.0619 · 0.2070 · 0.2520 |
(14,21,32) |
| 1 | 0.0623 · 0.2068 · 0.2522 |
(4,7,9) |
| 1 | 0.1360 · 0.3145 · 0.4480 |
(13,21,31) |
| 1 | 0.1368 · 0.3165 · 0.4509 |
(3,9,29) |
| 1 | 0.1548 · 0.3862 · 0.5396 |
(0,9,11) |
| 1 | 0.1557 · 0.3881 · 0.5424 |
(16,21,24) |
| 1 | 0.1951 · 0.3665 · 0.5604 |
(10,19,28) |
| 1 | 0.1954 · 0.3676 · 0.5618 |
(18,22,25) |
| 1 | 0.2068 · 0.3765 · 0.5822 |
(7,9,24) |
| 1 | 0.2070 · 0.3776 · 0.5836 |
(0,14,21) |
| 1 | 0.1976 · 0.3987 · 0.5953 |
(6,15,18) |
| 1 | 0.1979 · 0.4000 · 0.5969 |
(10,20,27) |
| 1 | 0.2520 · 0.3870 · 0.6382 |
(21,29,32) |
| 1 | 0.2522 · 0.3879 · 0.6394 |
(4,9,31) |
| 1 | 0.1917 · 0.4736 · 0.6645 |
(13,20,30) |
| 1 | 0.1919 · 0.4735 · 0.6646 |
(3,6,17) |
| 1 | 0.2479 · 0.4299 · 0.6771 |
(16,18,23) |
| 1 | 0.2493 · 0.4325 · 0.6811 |
(10,11,23) |
| 1 | 0.1627 · 0.5370 · 0.6989 |
(12,20,24) |
| 1 | 0.1637 · 0.5400 · 0.7029 |
(0,6,26) |
| 1 | 0.2399 · 0.4716 · 0.7108 |
(3,11,16) |
| 1 | 0.2401 · 0.4716 · 0.7111 |
(11,13,16) |
| 1 | 0.3533 · 0.3733 · 0.7262 |
(3,22,26) |
| 1 | 0.3546 · 0.3750 · 0.7291 |
(12,13,19) |
| 1 | 0.3346 · 0.3987 · 0.7328 |
(15,18,28) |
| 1 | 0.3339 · 0.4007 · 0.7341 |
(4,15,33) |
| 1 | 0.3360 · 0.4000 · 0.7355 |
(10,25,27) |
| 1 | 0.3353 · 0.4021 · 0.7370 |
(2,27,32) |
| 1 | 0.2638 · 0.4922 · 0.7555 |
(8,27,33) |
| 1 | 0.2652 · 0.4952 · 0.7599 |
(1,2,15) |
| 1 | 0.2877 · 0.5971 · 0.8845 |
(1,27,29) |
| 1 | 0.2891 · 0.6004 · 0.8892 |
(8,15,31) |
| 1 | 0.1558 · 0.7365 · 0.8919 |
(0,10,29) |
| 1 | 0.1560 · 0.7365 · 0.8921 |
(18,24,31) |
| 1 | 0.2408 · 0.6682 · 0.9087 |
(9,16,22) |
| 1 | 0.2410 · 0.6681 · 0.9088 |
(11,19,21) |
| 1 | 0.2002 · 0.7101 · 0.9100 |
(3,4,25) |
| 1 | 0.2005 · 0.7107 · 0.9108 |
(13,28,32) |
| 1 | 0.2455 · 0.6661 · 0.9113 |
(1,3,12) |
| 1 | 0.2467 · 0.6690 · 0.9154 |
(8,13,26) |
| 1 | 0.3625 · 0.5906 · 0.9529 |
(7,22,33) |
| 1 | 0.2520 · 0.7036 · 0.9553 |
(7,21,32) |
| 1 | 0.3634 · 0.5925 · 0.9556 |
(2,14,19) |
| 1 | 0.2522 · 0.7039 · 0.9558 |
(4,9,14) |
| 1 | 0.3709 · 0.5953 · 0.9659 |
(6,18,30) |
| 1 | 0.1627 · 0.8049 · 0.9672 |
(12,20,29) |
| 1 | 0.3717 · 0.5969 · 0.9684 |
(10,17,20) |
| 1 | 0.1637 · 0.8101 · 0.9734 |
(6,26,31) |
| 1 | 0.4652 · 0.5421 · 1.0071 |
(23,28,33) |
| 1 | 0.4681 · 0.5455 · 1.0135 |
(2,23,25) |
| 1 | 0.3427 · 0.6729 · 1.0154 |
(12,30,31) |
| 1 | 0.3440 · 0.6759 · 1.0197 |
(17,26,29) |
| 1 | 0.3274 · 0.7154 · 1.0427 |
(11,28,31) |
| 1 | 0.3287 · 0.7179 · 1.0465 |
(16,25,29) |
| 1 | 0.2653 · 0.8844 · 1.1495 |
(9,27,28) |
| 1 | 0.3884 · 0.7685 · 1.1568 |
(7,19,23) |
| 1 | 0.2670 · 0.8899 · 1.1568 |
(15,21,25) |
| 1 | 0.3936 · 0.7680 · 1.1614 |
(1,7,20) |
| 1 | 0.3909 · 0.7733 · 1.1641 |
(14,22,23) |
| 1 | 0.3961 · 0.7730 · 1.1689 |
(6,8,14) |
Provenance
- Found by Fable 5.1 with Shengtong Zhang, September 2026.
- Coordinates by an external contributor, re-verified here:
Fable51 search campaign, September 2026: symmetry-reduced basin hopping (orbit parametrization, ruin-and-recreate, soft-min L-BFGS warm-up, trust-region SLP polish); tie system refined to 80 digits by damped Gauss-Newton; verified in exact rational arithmetic— not symmetric, 62 tied minimal triangles; insertion ladder from the 33-point configuration (+1 point, asymmetric basin hopping). - Verified in exact arithmetic: all 5984 triples enumerated, 62 tied at the minimum.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
