Triangle, n = 31 record
A = 0.004755947961904…
full precision
Exact value of the published coordinate literals:
0.004755947961904655583311905866
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
57 triangles tied (within relative 10−9) at the minimal area, in 57 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0999 · 0.2013 · 0.2932 |
(7,9,23) |
| 1 | 0.0999 · 0.2221 · 0.3153 |
(5,7,9) |
| 1 | 0.1717 · 0.2434 · 0.4125 |
(15,21,30) |
| 1 | 0.1899 · 0.2437 · 0.4313 |
(20,23,24) |
| 1 | 0.1488 · 0.2866 · 0.4329 |
(13,22,30) |
| 1 | 0.1406 · 0.3194 · 0.4578 |
(2,17,29) |
| 1 | 0.1488 · 0.3210 · 0.4677 |
(22,28,30) |
| 1 | 0.2235 · 0.3099 · 0.5323 |
(5,6,20) |
| 1 | 0.2267 · 0.3145 · 0.5400 |
(11,13,15) |
| 1 | 0.1768 · 0.3689 · 0.5445 |
(8,26,30) |
| 1 | 0.2418 · 0.3046 · 0.5453 |
(0,3,29) |
| 1 | 0.2430 · 0.3281 · 0.5700 |
(11,17,30) |
| 1 | 0.2201 · 0.3655 · 0.5847 |
(1,2,6) |
| 1 | 0.2729 · 0.3266 · 0.5986 |
(6,9,29) |
| 1 | 0.1899 · 0.4205 · 0.6094 |
(20,24,30) |
| 1 | 0.2201 · 0.3939 · 0.6132 |
(2,6,23) |
| 1 | 0.2441 · 0.3711 · 0.6143 |
(25,27,29) |
| 1 | 0.0998 · 0.5818 · 0.6805 |
(4,6,28) |
| 1 | 0.3532 · 0.3652 · 0.7179 |
(7,15,24) |
| 1 | 0.2913 · 0.4413 · 0.7321 |
(4,11,22) |
| 1 | 0.2419 · 0.5085 · 0.7499 |
(3,22,26) |
| 1 | 0.2161 · 0.5482 · 0.7638 |
(7,10,29) |
| 1 | 0.2454 · 0.5224 · 0.7673 |
(18,21,29) |
| 1 | 0.2971 · 0.4929 · 0.7896 |
(15,17,28) |
| 1 | 0.2815 · 0.5232 · 0.8044 |
(7,20,21) |
| 1 | 0.3046 · 0.5064 · 0.8106 |
(0,3,6) |
| 1 | 0.1517 · 0.6626 · 0.8138 |
(3,21,25) |
| 1 | 0.2913 · 0.5261 · 0.8170 |
(4,16,22) |
| 1 | 0.3908 · 0.4365 · 0.8270 |
(3,8,27) |
| 1 | 0.3739 · 0.4578 · 0.8313 |
(12,14,15) |
| 1 | 0.2801 · 0.5572 · 0.8369 |
(1,5,27) |
| 1 | 0.1890 · 0.6626 · 0.8512 |
(3,13,21) |
| 1 | 0.3241 · 0.5335 · 0.8573 |
(12,21,26) |
| 1 | 0.1661 · 0.7121 · 0.8778 |
(0,8,20) |
| 1 | 0.2969 · 0.5959 · 0.8925 |
(12,13,16) |
| 1 | 0.4618 · 0.5139 · 0.9755 |
(14,21,24) |
| 1 | 0.3114 · 0.6673 · 0.9785 |
(2,3,10) |
| 1 | 0.4271 · 0.5533 · 0.9802 |
(4,27,30) |
| 1 | 0.2441 · 0.7413 · 0.9851 |
(20,25,27) |
| 1 | 0.2419 · 0.7596 · 1.0013 |
(1,22,26) |
| 1 | 0.0998 · 0.9236 · 1.0229 |
(4,23,28) |
| 1 | 0.3975 · 0.6267 · 1.0240 |
(3,16,30) |
| 1 | 0.4783 · 0.5572 · 1.0353 |
(1,5,14) |
| 1 | 0.4994 · 0.5536 · 1.0528 |
(7,18,27) |
| 1 | 0.4413 · 0.6448 · 1.0860 |
(11,22,25) |
| 1 | 0.1768 · 0.9287 · 1.1053 |
(7,26,30) |
| 1 | 0.4534 · 0.6547 · 1.1080 |
(19,24,29) |
| 1 | 0.2652 · 0.8433 · 1.1083 |
(7,14,25) |
| 1 | 0.1865 · 0.9230 · 1.1092 |
(9,10,30) |
| 1 | 0.4205 · 0.7008 · 1.1211 |
(14,20,30) |
| 1 | 0.3288 · 0.8409 · 1.1695 |
(0,16,28) |
| 1 | 0.5232 · 0.6769 · 1.2000 |
(7,11,20) |
| 1 | 0.4189 · 0.8369 · 1.2557 |
(5,10,27) |
| 1 | 0.5147 · 0.7485 · 1.2631 |
(11,19,28) |
| 1 | 0.4578 · 0.8925 · 1.3502 |
(12,14,16) |
| 1 | 0.2969 · 1.0597 · 1.3564 |
(10,13,16) |
| 1 | 0.5660 · 0.8166 · 1.3824 |
(14,18,19) |
Provenance
- Found by Tej Stead, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-07-25/triangle-n31. - Verified in exact arithmetic: all 4495 triples enumerated, 57 tied at the minimum.
- Friedman's page lists:
A = .004755+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
