Triangle, n = 32 record
A = 0.004800755460787…
full precision
Exact value of the published coordinate literals:
0.00480075546078703997314265850182
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
59 triangles tied (within relative 10−9) at the minimal area, in 59 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1110 · 0.1146 · 0.2053 |
(7,12,22) |
| 1 | 0.1572 · 0.2494 · 0.4036 |
(0,7,20) |
| 1 | 0.1574 · 0.2494 · 0.4039 |
(1,3,11) |
| 1 | 0.1580 · 0.2511 · 0.4061 |
(14,15,27) |
| 1 | 0.1582 · 0.2593 · 0.4147 |
(5,8,18) |
| 1 | 0.1652 · 0.2556 · 0.4182 |
(6,9,16) |
| 1 | 0.1053 · 0.3361 · 0.4383 |
(13,15,23) |
| 1 | 0.1068 · 0.3360 · 0.4398 |
(19,22,26) |
| 1 | 0.1085 · 0.3411 · 0.4468 |
(6,24,30) |
| 1 | 0.1146 · 0.3442 · 0.4563 |
(7,12,25) |
| 1 | 0.1131 · 0.3458 · 0.4563 |
(8,10,21) |
| 1 | 0.2247 · 0.3424 · 0.5660 |
(2,14,28) |
| 1 | 0.2232 · 0.3484 · 0.5705 |
(4,25,31) |
| 1 | 0.2261 · 0.3570 · 0.5821 |
(0,26,29) |
| 1 | 0.2275 · 0.3610 · 0.5876 |
(2,5,24) |
| 1 | 0.2608 · 0.4133 · 0.6734 |
(0,17,28) |
| 1 | 0.1930 · 0.5581 · 0.7506 |
(0,24,25) |
| 1 | 0.3522 · 0.4383 · 0.7902 |
(10,13,23) |
| 1 | 0.3576 · 0.4398 · 0.7970 |
(22,24,26) |
| 1 | 0.3576 · 0.4468 · 0.8040 |
(24,26,30) |
| 1 | 0.3553 · 0.4494 · 0.8043 |
(4,7,16) |
| 1 | 0.3622 · 0.4456 · 0.8075 |
(1,5,14) |
| 1 | 0.3522 · 0.4563 · 0.8082 |
(10,21,23) |
| 1 | 0.3527 · 0.4563 · 0.8087 |
(12,25,28) |
| 1 | 0.3361 · 0.4801 · 0.8158 |
(15,18,23) |
| 1 | 0.3553 · 0.4616 · 0.8166 |
(4,8,16) |
| 1 | 0.3634 · 0.4543 · 0.8173 |
(0,3,15) |
| 1 | 0.3416 · 0.4770 · 0.8182 |
(1,10,27) |
| 1 | 0.3492 · 0.4728 · 0.8217 |
(11,15,25) |
| 1 | 0.3458 · 0.4770 · 0.8224 |
(8,10,27) |
| 1 | 0.3622 · 0.4674 · 0.8293 |
(5,6,14) |
| 1 | 0.3634 · 0.4663 · 0.8293 |
(0,3,19) |
| 1 | 0.3634 · 0.4801 · 0.8432 |
(6,18,23) |
| 1 | 0.3619 · 0.4856 · 0.8472 |
(19,20,28) |
| 1 | 0.3786 · 0.5877 · 0.9661 |
(9,12,17) |
| 1 | 0.3786 · 0.5906 · 0.9690 |
(11,13,20) |
| 1 | 0.3868 · 0.5877 · 0.9743 |
(9,17,21) |
| 1 | 0.3920 · 0.5906 · 0.9824 |
(11,20,22) |
| 1 | 0.3939 · 0.5888 · 0.9825 |
(18,27,30) |
| 1 | 0.4036 · 0.5943 · 0.9977 |
(0,2,7) |
| 1 | 0.4147 · 0.5880 · 1.0025 |
(5,8,29) |
| 1 | 0.4039 · 0.6017 · 1.0054 |
(1,3,31) |
| 1 | 0.4182 · 0.5894 · 1.0074 |
(6,16,29) |
| 1 | 0.4061 · 0.6054 · 1.0113 |
(14,15,31) |
| 1 | 0.4186 · 0.5958 · 1.0142 |
(2,4,19) |
| 1 | 0.2057 · 0.8624 · 1.0678 |
(1,4,26) |
| 1 | 0.3477 · 0.7406 · 1.0881 |
(12,20,27) |
| 1 | 0.5289 · 0.6331 · 1.1619 |
(6,7,31) |
| 1 | 0.5230 · 0.6421 · 1.1650 |
(7,15,29) |
| 1 | 0.5199 · 0.6586 · 1.1784 |
(2,6,15) |
| 1 | 0.3319 · 0.8724 · 1.2042 |
(1,22,28) |
| 1 | 0.6336 · 0.6380 · 1.2715 |
(1,2,21) |
| 1 | 0.6244 · 0.6514 · 1.2758 |
(8,22,31) |
| 1 | 0.4468 · 0.8492 · 1.2959 |
(12,24,30) |
| 1 | 0.4563 · 0.8462 · 1.3024 |
(12,13,25) |
| 1 | 0.4398 · 0.8671 · 1.3068 |
(21,22,26) |
| 1 | 0.4383 · 0.8687 · 1.3069 |
(13,23,30) |
| 1 | 0.6670 · 0.6855 · 1.3524 |
(12,21,31) |
| 1 | 0.6722 · 0.6884 · 1.3605 |
(13,22,29) |
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; 59 tied minimal triangles. - Verified in exact arithmetic: all 4960 triples enumerated, 59 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
