Convex, n = 34 record
A = 0.005206216986514…
full precision
Exact value of the published coordinate literals:
0.00520621698651450222548950311494
Symmetry
Symmetry
2-fold dihedral symmetry (group D2, order 4).
34 points in 9 orbits (4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 2) — hover a point to see its orbit.
Minimal triangles
62 triangles tied (within relative 10−9) at the minimal area, in 16 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 4 | 0.0833 · 0.0991 · 0.1546 |
(8,14,30) (9,15,31) (10,12,28) (11,13,29) |
| 4 | 0.1196 · 0.1546 · 0.2684 |
(12,22,28) (13,23,29) (14,20,30) (15,21,31) |
| 4 | 0.0833 · 0.2331 · 0.3116 |
(8,18,30) (9,19,31) (10,16,28) (11,17,29) |
| 4 | 0.1056 · 0.2391 · 0.3414 |
(0,15,19) (1,14,18) (2,13,17) (3,12,16) |
| 4 | 0.1546 · 0.2482 · 0.4010 |
(12,28,33) (13,29,32) (14,30,33) (15,31,32) |
| 4 | 0.1056 · 0.4385 · 0.5430 |
(0,19,32) (1,18,33) (2,17,32) (3,16,33) |
| 4 | 0.1650 · 0.4010 · 0.5653 |
(20,28,33) (21,29,32) (22,30,33) (23,31,32) |
| 4 | 0.2209 · 0.4582 · 0.6787 |
(4,14,24) (5,15,25) (6,12,26) (7,13,27) |
| 4 | 0.1578 · 0.5510 · 0.7084 |
(0,12,31) (1,13,30) (2,14,29) (3,15,28) |
| 4 | 0.0991 · 0.6416 · 0.7401 |
(8,14,28) (9,15,29) (10,12,30) (11,13,31) |
| 4 | 0.2845 · 0.4959 · 0.7802 |
(0,5,29) (1,4,28) (2,7,31) (3,6,30) |
| 4 | 0.3338 · 0.4835 · 0.8171 |
(16,23,24) (17,22,25) (18,21,26) (19,20,27) |
| 4 | 0.2071 · 0.6542 · 0.8611 |
(4,11,33) (5,10,32) (6,9,33) (7,8,32) |
| 4 | 0.2646 · 0.6787 · 0.9432 |
(12,26,29) (13,27,28) (14,24,31) (15,25,30) |
| 4 | 0.2646 · 0.7602 · 1.0247 |
(8,24,31) (9,25,30) (10,26,29) (11,27,28) |
| 2 | 0.3439 · 0.3439 · 0.6874 |
(8,10,33) (9,11,32) |
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— 2-fold dihedral symmetric; 62 tied minimal triangles. - 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
