Triangle, n = 26 record
A = 0.007471569726815…
full precision
Exact value of the published coordinate literals:
0.00747156972681512236815605390391
Symmetry
Symmetry
Mirror symmetric (group D1, order 2).
26 points in 14 orbits (2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 1 + 1) — hover a point to see its orbit.
Minimal triangles
48 triangles tied (within relative 10−9) at the minimal area, in 24 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 2 | 0.1895 · 0.2059 · 0.3878 |
(8,14,15) (11,19,22) |
| 2 | 0.1888 · 0.2911 · 0.4756 |
(7,12,15) (9,19,23) |
| 2 | 0.1934 · 0.2999 · 0.4892 |
(2,13,16) (5,6,20) |
| 2 | 0.1888 · 0.3093 · 0.4942 |
(0,12,15) (0,19,23) |
| 2 | 0.1884 · 0.3109 · 0.4955 |
(10,11,21) (14,24,25) |
| 2 | 0.1884 · 0.3126 · 0.4972 |
(0,10,11) (0,14,24) |
| 2 | 0.2561 · 0.3599 · 0.6140 |
(1,4,12) (4,17,23) |
| 2 | 0.1934 · 0.6625 · 0.8549 |
(2,4,16) (4,5,20) |
| 2 | 0.4177 · 0.4434 · 0.8604 |
(1,3,25) (17,18,21) |
| 2 | 0.4313 · 0.4423 · 0.8730 |
(7,8,22) (8,9,22) |
| 2 | 0.1871 · 0.7267 · 0.9129 |
(1,19,24) (10,15,17) |
| 2 | 0.2081 · 0.7197 · 0.9270 |
(2,14,18) (3,11,20) |
| 2 | 0.3743 · 0.6522 · 1.0261 |
(4,7,19) (4,9,15) |
| 2 | 0.3138 · 0.7256 · 1.0390 |
(5,7,14) (9,11,16) |
| 2 | 0.3275 · 0.7256 · 1.0527 |
(5,13,14) (6,11,16) |
| 2 | 0.5130 · 0.5424 · 1.0551 |
(10,12,25) (21,23,24) |
| 2 | 0.3699 · 0.7715 · 1.1411 |
(0,4,6) (0,4,13) |
| 2 | 0.2702 · 0.8754 · 1.1452 |
(6,15,24) (10,13,19) |
| 2 | 0.2838 · 0.8809 · 1.1644 |
(2,5,21) (16,20,25) |
| 2 | 0.4756 · 0.7274 · 1.2027 |
(1,9,23) (7,12,17) |
| 2 | 0.4892 · 0.7358 · 1.2248 |
(2,13,22) (6,8,20) |
| 2 | 0.4955 · 0.7417 · 1.2369 |
(3,10,21) (18,24,25) |
| 2 | 0.4465 · 0.8604 · 1.3067 |
(3,6,25) (13,18,21) |
| 2 | 0.6522 · 0.7089 · 1.3610 |
(4,7,21) (4,9,25) |
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; 48 tied minimal triangles. - Verified in exact arithmetic: all 2600 triples enumerated, 48 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
