Square, n = 33 record
A = 0.005071344158467…
full precision
Exact value of the published coordinate literals:
0.00507134415846717570830533095150
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
56 triangles tied (within relative 10−9) at the minimal area, in 56 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0668 · 0.1816 · 0.2254 |
(3,4,8) |
| 1 | 0.0690 · 0.1929 · 0.2433 |
(19,28,30) |
| 1 | 0.0668 · 0.2055 · 0.2553 |
(3,4,26) |
| 1 | 0.1827 · 0.2004 · 0.3793 |
(2,11,24) |
| 1 | 0.1899 · 0.3533 · 0.5418 |
(2,20,30) |
| 1 | 0.2055 · 0.3690 · 0.5733 |
(3,24,26) |
| 1 | 0.2066 · 0.3756 · 0.5810 |
(0,9,14) |
| 1 | 0.1982 · 0.3915 · 0.5886 |
(10,20,27) |
| 1 | 0.2553 · 0.3715 · 0.6260 |
(4,26,31) |
| 1 | 0.1899 · 0.4570 · 0.6460 |
(13,20,30) |
| 1 | 0.2447 · 0.4138 · 0.6577 |
(10,11,23) |
| 1 | 0.2487 · 0.4284 · 0.6764 |
(6,11,21) |
| 1 | 0.2066 · 0.4875 · 0.6933 |
(9,14,26) |
| 1 | 0.2522 · 0.4436 · 0.6952 |
(16,18,23) |
| 1 | 0.1787 · 0.5195 · 0.6974 |
(0,21,29) |
| 1 | 0.1517 · 0.5559 · 0.7067 |
(12,20,24) |
| 1 | 0.3451 · 0.3636 · 0.7082 |
(16,17,21) |
| 1 | 0.2425 · 0.4669 · 0.7088 |
(11,13,16) |
| 1 | 0.2575 · 0.4525 · 0.7094 |
(1,12,16) |
| 1 | 0.3337 · 0.3781 · 0.7112 |
(2,27,32) |
| 1 | 0.2494 · 0.4669 · 0.7157 |
(8,11,16) |
| 1 | 0.1563 · 0.5783 · 0.7339 |
(18,19,21) |
| 1 | 0.3382 · 0.4076 · 0.7453 |
(15,18,28) |
| 1 | 0.2559 · 0.4980 · 0.7533 |
(0,5,27) |
| 1 | 0.3622 · 0.3938 · 0.7555 |
(8,21,22) |
| 1 | 0.3705 · 0.3915 · 0.7615 |
(10,25,27) |
| 1 | 0.2716 · 0.4980 · 0.7691 |
(5,27,28) |
| 1 | 0.3691 · 0.4009 · 0.7695 |
(10,19,29) |
| 1 | 0.2904 · 0.4895 · 0.7794 |
(1,15,17) |
| 1 | 0.2922 · 0.5792 · 0.8711 |
(6,15,31) |
| 1 | 0.1601 · 0.7286 · 0.8882 |
(18,24,31) |
| 1 | 0.1976 · 0.6935 · 0.8907 |
(13,28,32) |
| 1 | 0.1899 · 0.7065 · 0.8960 |
(14,20,30) |
| 1 | 0.2487 · 0.6560 · 0.9044 |
(6,13,21) |
| 1 | 0.2428 · 0.6620 · 0.9044 |
(9,11,19) |
| 1 | 0.1965 · 0.7176 · 0.9137 |
(3,17,29) |
| 1 | 0.3710 · 0.5693 · 0.9400 |
(2,14,19) |
| 1 | 0.2575 · 0.6885 · 0.9457 |
(1,8,12) |
| 1 | 0.2553 · 0.6933 · 0.9484 |
(4,14,26) |
| 1 | 0.2055 · 0.7467 · 0.9518 |
(3,26,32) |
| 1 | 0.3990 · 0.5596 · 0.9584 |
(21,25,26) |
| 1 | 0.1787 · 0.7848 · 0.9631 |
(21,29,31) |
| 1 | 0.4068 · 0.5886 · 0.9952 |
(10,17,20) |
| 1 | 0.3749 · 0.6232 · 0.9979 |
(18,29,30) |
| 1 | 0.4695 · 0.5459 · 1.0152 |
(0,1,30) |
| 1 | 0.3301 · 0.6954 · 1.0254 |
(12,30,31) |
| 1 | 0.4693 · 0.5629 · 1.0320 |
(3,5,12) |
| 1 | 0.3371 · 0.7158 · 1.0528 |
(11,28,31) |
| 1 | 0.5707 · 0.5875 · 1.1580 |
(13,23,25) |
| 1 | 0.4104 · 0.7484 · 1.1586 |
(6,14,29) |
| 1 | 0.5459 · 0.6141 · 1.1599 |
(1,26,30) |
| 1 | 0.3905 · 0.7794 · 1.1698 |
(1,13,17) |
| 1 | 0.5611 · 0.6144 · 1.1754 |
(4,6,19) |
| 1 | 0.3982 · 0.7792 · 1.1773 |
(3,19,23) |
| 1 | 0.3985 · 0.7945 · 1.1929 |
(1,4,20) |
| 1 | 0.2745 · 0.9238 · 1.1981 |
(8,27,30) |
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, 56 tied minimal triangles; insertion ladder: the n=32 D4 record plus one greedily inserted point, re-optimized by asymmetric basin hopping. - Verified in exact arithmetic: all 5456 triples enumerated, 56 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
