Triangle, n = 35 record
A = 0.004032684320705…
full precision
Exact value of the published coordinate literals:
0.00403268432070586439072011996014
Symmetry
Symmetry
Mirror symmetric (group D1, order 2).
35 points in 18 orbits (2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 1) — hover a point to see its orbit.
Minimal triangles
65 triangles tied (within relative 10−9) at the minimal area, in 33 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 2 | 0.1529 · 0.2087 · 0.3587 |
(0,12,17) (1,13,16) |
| 2 | 0.2040 · 0.2524 · 0.4550 |
(10,25,34) (11,24,34) |
| 2 | 0.1715 · 0.2970 · 0.4671 |
(0,20,31) (1,21,30) |
| 2 | 0.1768 · 0.3518 · 0.5275 |
(4,12,22) (5,13,23) |
| 2 | 0.1477 · 0.4097 · 0.5565 |
(16,20,21) (17,20,21) |
| 2 | 0.2895 · 0.3692 · 0.6582 |
(2,7,26) (3,6,27) |
| 2 | 0.1273 · 0.5327 · 0.6592 |
(4,27,31) (5,26,30) |
| 2 | 0.2040 · 0.4570 · 0.6604 |
(0,11,34) (1,10,34) |
| 2 | 0.1429 · 0.5271 · 0.6694 |
(8,14,26) (9,15,27) |
| 2 | 0.2640 · 0.4537 · 0.7173 |
(0,22,33) (1,23,32) |
| 2 | 0.1517 · 0.6041 · 0.7554 |
(4,19,26) (5,18,27) |
| 2 | 0.2606 · 0.6340 · 0.8944 |
(10,14,21) (11,15,20) |
| 2 | 0.2690 · 0.6507 · 0.9195 |
(6,32,34) (7,33,34) |
| 2 | 0.4341 · 0.5035 · 0.9375 |
(22,28,34) (23,29,34) |
| 2 | 0.3502 · 0.6302 · 0.9802 |
(12,16,31) (13,17,30) |
| 2 | 0.3171 · 0.6680 · 0.9850 |
(18,25,31) (19,24,30) |
| 2 | 0.1715 · 0.8380 · 1.0093 |
(0,5,31) (1,4,30) |
| 2 | 0.3284 · 0.6866 · 1.0149 |
(14,16,32) (15,17,33) |
| 2 | 0.4789 · 0.5463 · 1.0251 |
(2,5,24) (3,4,25) |
| 2 | 0.2928 · 0.7407 · 1.0334 |
(6,14,25) (7,15,24) |
| 2 | 0.4098 · 0.6440 · 1.0537 |
(20,23,28) (21,22,29) |
| 2 | 0.4683 · 0.6245 · 1.0927 |
(12,14,34) (13,15,34) |
| 2 | 0.2370 · 0.9290 · 1.1659 |
(2,4,16) (3,5,17) |
| 2 | 0.3284 · 0.8439 · 1.1722 |
(14,30,32) (15,31,33) |
| 2 | 0.4306 · 0.7538 · 1.1844 |
(8,10,13) (9,11,12) |
| 2 | 0.3530 · 0.8444 · 1.1973 |
(0,8,25) (1,9,24) |
| 2 | 0.3198 · 0.9064 · 1.2261 |
(10,26,28) (11,27,29) |
| 2 | 0.5271 · 0.7041 · 1.2312 |
(14,26,29) (15,27,28) |
| 2 | 0.5053 · 0.7859 · 1.2911 |
(6,20,29) (7,21,28) |
| 2 | 0.6582 · 0.6694 · 1.3275 |
(2,8,26) (3,9,27) |
| 2 | 0.6680 · 0.6692 · 1.3371 |
(8,18,31) (9,19,30) |
| 2 | 0.5475 · 0.8424 · 1.3898 |
(2,12,28) (3,13,29) |
| 1 | 0.3670 · 0.3670 · 0.7338 |
(26,27,34) |
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— mirror symmetric (swap of the two legs); 65 tied minimal triangles. - Verified in exact arithmetic: all 6545 triples enumerated, 65 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
