Convex, n = 29 record
A = 0.007289115327459…
full precision
Exact value of the published coordinate literals:
0.00728911532745986489525489343543
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
52 triangles tied (within relative 10−9) at the minimal area, in 52 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1559 · 0.2096 · 0.3619 |
(2,14,28) |
| 1 | 0.1559 · 0.2129 · 0.3652 |
(2,9,14) |
| 1 | 0.1676 · 0.2013 · 0.3654 |
(5,6,17) |
| 1 | 0.1634 · 0.2114 · 0.3715 |
(1,9,16) |
| 1 | 0.1729 · 0.2032 · 0.3728 |
(0,20,24) |
| 1 | 0.1729 · 0.2048 · 0.3744 |
(20,21,24) |
| 1 | 0.1676 · 0.2107 · 0.3750 |
(5,17,28) |
| 1 | 0.1419 · 0.2491 · 0.3879 |
(7,24,27) |
| 1 | 0.1566 · 0.2425 · 0.3963 |
(0,13,26) |
| 1 | 0.1396 · 0.2635 · 0.4001 |
(2,16,18) |
| 1 | 0.1356 · 0.2684 · 0.4010 |
(5,11,27) |
| 1 | 0.1641 · 0.2437 · 0.4052 |
(3,9,25) |
| 1 | 0.1377 · 0.2704 · 0.4052 |
(8,16,24) |
| 1 | 0.1400 · 0.2714 · 0.4087 |
(14,17,19) |
| 1 | 0.1394 · 0.2875 · 0.4243 |
(7,11,17) |
| 1 | 0.1419 · 0.2983 · 0.4378 |
(1,18,19) |
| 1 | 0.1388 · 0.3021 · 0.4385 |
(8,18,20) |
| 1 | 0.1396 · 0.3021 · 0.4393 |
(2,8,18) |
| 1 | 0.1356 · 0.3150 · 0.4484 |
(11,19,27) |
| 1 | 0.1377 · 0.3169 · 0.4524 |
(7,8,16) |
| 1 | 0.2096 · 0.3945 · 0.6032 |
(1,14,28) |
| 1 | 0.2032 · 0.4052 · 0.6075 |
(0,16,24) |
| 1 | 0.2114 · 0.3970 · 0.6076 |
(1,9,20) |
| 1 | 0.2013 · 0.4087 · 0.6091 |
(6,14,17) |
| 1 | 0.2129 · 0.3988 · 0.6108 |
(2,5,9) |
| 1 | 0.2107 · 0.4010 · 0.6109 |
(5,27,28) |
| 1 | 0.2754 · 0.3478 · 0.6225 |
(7,13,20) |
| 1 | 0.2946 · 0.3495 · 0.6434 |
(0,23,27) |
| 1 | 0.2024 · 0.4576 · 0.6592 |
(16,21,25) |
| 1 | 0.2934 · 0.3715 · 0.6643 |
(9,16,22) |
| 1 | 0.1377 · 0.5294 · 0.6662 |
(8,16,26) |
| 1 | 0.2013 · 0.4669 · 0.6676 |
(3,6,17) |
| 1 | 0.2986 · 0.3750 · 0.6731 |
(13,17,28) |
| 1 | 0.1400 · 0.5356 · 0.6747 |
(13,14,19) |
| 1 | 0.3574 · 0.3716 · 0.7286 |
(4,8,10) |
| 1 | 0.1087 · 0.6344 · 0.7422 |
(5,15,24) |
| 1 | 0.1085 · 0.6377 · 0.7454 |
(3,14,20) |
| 1 | 0.1118 · 0.6382 · 0.7491 |
(17,20,22) |
| 1 | 0.1120 · 0.6426 · 0.7538 |
(5,12,16) |
| 1 | 0.1078 · 0.6523 · 0.7593 |
(2,25,27) |
| 1 | 0.1141 · 0.6491 · 0.7625 |
(1,17,23) |
| 1 | 0.1154 · 0.6489 · 0.7635 |
(13,16,27) |
| 1 | 0.1196 · 0.6465 · 0.7653 |
(2,10,24) |
| 1 | 0.1087 · 0.6696 · 0.7775 |
(5,15,20) |
| 1 | 0.1085 · 0.6716 · 0.7794 |
(3,14,24) |
| 1 | 0.1118 · 0.6696 · 0.7806 |
(5,20,22) |
| 1 | 0.1120 · 0.6756 · 0.7869 |
(12,16,17) |
| 1 | 0.1141 · 0.6756 · 0.7890 |
(16,17,23) |
| 1 | 0.1196 · 0.6716 · 0.7905 |
(10,14,24) |
| 1 | 0.1118 · 0.6844 · 0.7956 |
(1,4,27) |
| 1 | 0.1154 · 0.6844 · 0.7991 |
(1,13,27) |
| 1 | 0.1078 · 0.7863 · 0.8935 |
(2,25,26) |
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, greedy ruin-and-recreate, soft-min warm-up, trust-region SLP) and insertion ladders from neighbouring records; tie system refined to 80 digits by damped Gauss-Newton; verified in exact rational arithmetic— not symmetric; 52 tied minimal triangles. - Verified in exact arithmetic: all 3654 triples enumerated, 52 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
