Triangle, n = 29 record
A = 0.006123691184844…
full precision
Exact value of the published coordinate literals:
0.00612369118484431967312891224509
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
53 triangles tied (within relative 10−9) at the minimal area, in 53 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1082 · 0.2502 · 0.3501 |
(3,7,23) |
| 1 | 0.1082 · 0.2747 · 0.3760 |
(3,7,15) |
| 1 | 0.1195 · 0.2719 · 0.3853 |
(5,6,25) |
| 1 | 0.1684 · 0.2747 · 0.4394 |
(7,15,21) |
| 1 | 0.1782 · 0.2976 · 0.4728 |
(2,3,26) |
| 1 | 0.1135 · 0.3661 · 0.4757 |
(10,11,20) |
| 1 | 0.1177 · 0.3627 · 0.4766 |
(9,13,22) |
| 1 | 0.1782 · 0.3033 · 0.4786 |
(0,4,27) |
| 1 | 0.1487 · 0.3936 · 0.5400 |
(5,10,14) |
| 1 | 0.1613 · 0.3939 · 0.5531 |
(19,23,26) |
| 1 | 0.1495 · 0.4119 · 0.5592 |
(18,25,28) |
| 1 | 0.1135 · 0.4544 · 0.5653 |
(8,10,20) |
| 1 | 0.1541 · 0.4136 · 0.5657 |
(11,24,27) |
| 1 | 0.1613 · 0.4136 · 0.5729 |
(13,23,26) |
| 1 | 0.1495 · 0.4266 · 0.5740 |
(12,25,28) |
| 1 | 0.1177 · 0.4634 · 0.5786 |
(7,9,22) |
| 1 | 0.2917 · 0.3897 · 0.6804 |
(9,17,18) |
| 1 | 0.2407 · 0.4607 · 0.7005 |
(13,16,24) |
| 1 | 0.3052 · 0.4062 · 0.7105 |
(10,18,19) |
| 1 | 0.2728 · 0.4545 · 0.7265 |
(11,14,16) |
| 1 | 0.2807 · 0.4607 · 0.7406 |
(13,15,16) |
| 1 | 0.2899 · 0.4546 · 0.7437 |
(12,14,15) |
| 1 | 0.3033 · 0.4719 · 0.7746 |
(0,4,10) |
| 1 | 0.2976 · 0.4953 · 0.7922 |
(2,3,9) |
| 1 | 0.3246 · 0.5127 · 0.8367 |
(2,5,15) |
| 1 | 0.3874 · 0.4634 · 0.8503 |
(7,22,26) |
| 1 | 0.3944 · 0.4719 · 0.8658 |
(4,10,28) |
| 1 | 0.4072 · 0.4757 · 0.8824 |
(9,10,11) |
| 1 | 0.4051 · 0.4953 · 0.9000 |
(3,9,27) |
| 1 | 0.2345 · 0.6912 · 0.9252 |
(8,11,21) |
| 1 | 0.1916 · 0.7369 · 0.9280 |
(4,15,19) |
| 1 | 0.4136 · 0.6177 · 1.0311 |
(6,11,24) |
| 1 | 0.4119 · 0.6213 · 1.0329 |
(18,22,25) |
| 1 | 0.4266 · 0.6181 · 1.0445 |
(7,12,25) |
| 1 | 0.3939 · 0.6526 · 1.0463 |
(19,20,23) |
| 1 | 0.4117 · 0.6368 · 1.0482 |
(17,21,24) |
| 1 | 0.4136 · 0.6393 · 1.0527 |
(8,13,23) |
| 1 | 0.2393 · 0.8380 · 1.0770 |
(5,12,24) |
| 1 | 0.3749 · 0.7265 · 1.1011 |
(14,16,28) |
| 1 | 0.2600 · 0.8427 · 1.1024 |
(4,11,23) |
| 1 | 0.3769 · 0.7437 · 1.1204 |
(14,15,26) |
| 1 | 0.3837 · 0.7406 · 1.1241 |
(15,16,27) |
| 1 | 0.3240 · 0.8203 · 1.1440 |
(0,1,14) |
| 1 | 0.3246 · 0.8259 · 1.1503 |
(1,2,15) |
| 1 | 0.5011 · 0.6668 · 1.1677 |
(0,20,28) |
| 1 | 0.3348 · 0.8377 · 1.1722 |
(0,2,16) |
| 1 | 0.4920 · 0.6854 · 1.1772 |
(1,21,26) |
| 1 | 0.3139 · 0.8683 · 1.1820 |
(6,18,27) |
| 1 | 0.3085 · 0.8825 · 1.1908 |
(7,19,28) |
| 1 | 0.3298 · 0.8813 · 1.2108 |
(8,17,26) |
| 1 | 0.3749 · 0.8547 · 1.2295 |
(9,14,28) |
| 1 | 0.3769 · 0.8774 · 1.2541 |
(10,15,26) |
| 1 | 0.4920 · 0.8616 · 1.3534 |
(21,26,28) |
Provenance
- Found by Marc-Emmanuel Coupvent des Graviers, September 2026.
- Coordinates by an external contributor, re-verified here:
One-point deletion from the n=30 record, refined to 120 digits by Gauss-Newton— No symmetry; obtained by deleting one point of the n=30 record (Fable 5.1 with Shengtong Zhang): two points on each side, 53 minimal triangles, rigid (rank 53/53).. - Verified in exact arithmetic: all 3654 triples enumerated, 53 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
