Triangle, n = 30 record
A = 0.005957401091748…
full precision
Exact value of the published coordinate literals:
0.00595740109174871572421053510126
Symmetry
Symmetry
120° Rotationally symmetric (group C3, order 3).
30 points in 10 orbits (3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3) — hover a point to see its orbit.
Minimal triangles
57 triangles tied (within relative 10−9) at the minimal area, in 19 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 3 | 0.1145 · 0.3639 · 0.4747 |
(9,13,22) (10,14,23) (11,12,21) |
| 3 | 0.1760 · 0.3068 · 0.4801 |
(0,4,28) (1,5,29) (2,3,27) |
| 3 | 0.1505 · 0.4075 · 0.5559 |
(18,25,28) (19,26,29) (20,24,27) |
| 3 | 0.1505 · 0.4174 · 0.5658 |
(12,25,28) (13,26,29) (14,24,27) |
| 3 | 0.1145 · 0.4555 · 0.5676 |
(6,9,22) (7,10,23) (8,11,21) |
| 3 | 0.2960 · 0.3942 · 0.6893 |
(9,18,20) (10,18,19) (11,19,20) |
| 3 | 0.2798 · 0.4555 · 0.7345 |
(12,15,17) (13,15,16) (14,16,17) |
| 3 | 0.3068 · 0.4767 · 0.7829 |
(0,4,11) (1,5,9) (2,3,10) |
| 3 | 0.3875 · 0.4555 · 0.8426 |
(6,22,29) (7,23,27) (8,21,28) |
| 3 | 0.3922 · 0.4767 · 0.8684 |
(3,10,28) (4,11,29) (5,9,27) |
| 3 | 0.4128 · 0.4747 · 0.8871 |
(9,10,14) (9,11,13) (10,11,12) |
| 3 | 0.2288 · 0.6769 · 0.9051 |
(6,13,23) (7,14,21) (8,12,22) |
| 3 | 0.4075 · 0.6304 · 1.0377 |
(18,22,25) (19,23,26) (20,21,24) |
| 3 | 0.4174 · 0.6232 · 1.0403 |
(6,12,25) (7,13,26) (8,14,24) |
| 3 | 0.3740 · 0.7345 · 1.1083 |
(15,16,27) (15,17,29) (16,17,28) |
| 3 | 0.3235 · 0.8252 · 1.1484 |
(0,1,15) (0,2,17) (1,2,16) |
| 3 | 0.5004 · 0.6736 · 1.1739 |
(0,21,29) (1,22,27) (2,23,28) |
| 3 | 0.3184 · 0.8695 · 1.1876 |
(6,19,28) (7,20,29) (8,18,27) |
| 3 | 0.3740 · 0.8619 · 1.2357 |
(9,17,28) (10,15,29) (11,16,27) |
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— 3-fold rotationally symmetric; 57 tied minimal triangles. - Verified in exact arithmetic: all 4060 triples enumerated, 57 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
