Convex, n = 29 record
A = 0.006078819720691…
full precision
Exact value of the published coordinate literals:
0.00607881972069170544897354405764
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: no symmetry.)
Minimal triangles
52 triangles tied (within relative 10−9) at the minimal area, in 52 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1487 · 0.4216 · 0.5682 |
(7,12,20) |
| 1 | 0.1493 · 0.4239 · 0.5712 |
(6,11,19) |
| 1 | 0.1506 · 0.4253 · 0.5739 |
(25,26,27) |
| 1 | 0.1954 · 0.4469 · 0.6410 |
(13,21,26) |
| 1 | 0.2009 · 0.4465 · 0.6461 |
(15,16,18) |
| 1 | 0.1968 · 0.4509 · 0.6464 |
(12,13,14) |
| 1 | 0.2021 · 0.4456 · 0.6464 |
(8,16,23) |
| 1 | 0.2014 · 0.4465 · 0.6466 |
(15,16,17) |
| 1 | 0.2024 · 0.4456 · 0.6467 |
(3,8,16) |
| 1 | 0.2016 · 0.4469 · 0.6472 |
(8,15,22) |
| 1 | 0.1975 · 0.4516 · 0.6478 |
(4,11,22) |
| 1 | 0.2007 · 0.4491 · 0.6485 |
(14,21,27) |
| 1 | 0.2007 · 0.4491 · 0.6486 |
(7,14,21) |
| 1 | 0.2032 · 0.4469 · 0.6489 |
(2,8,15) |
| 1 | 0.1411 · 0.5984 · 0.7384 |
(4,6,14) |
| 1 | 0.1510 · 0.5890 · 0.7388 |
(14,26,28) |
| 1 | 0.1499 · 0.5916 · 0.7404 |
(10,12,21) |
| 1 | 0.1519 · 0.5907 · 0.7415 |
(9,11,21) |
| 1 | 0.1543 · 0.5902 · 0.7433 |
(8,18,20) |
| 1 | 0.1526 · 0.5920 · 0.7434 |
(15,23,25) |
| 1 | 0.1532 · 0.5921 · 0.7442 |
(16,22,24) |
| 1 | 0.1530 · 0.5924 · 0.7443 |
(8,17,19) |
| 1 | 0.1552 · 0.5920 · 0.7461 |
(1,2,16) |
| 1 | 0.1559 · 0.5927 · 0.7476 |
(0,3,15) |
| 1 | 0.1549 · 0.5963 · 0.7501 |
(5,7,13) |
| 1 | 0.3478 · 0.5369 · 0.8842 |
(11,15,28) |
| 1 | 0.3465 · 0.5396 · 0.8856 |
(4,15,27) |
| 1 | 0.3467 · 0.5459 · 0.8921 |
(5,16,26) |
| 1 | 0.3524 · 0.5410 · 0.8929 |
(6,8,10) |
| 1 | 0.3508 · 0.5429 · 0.8932 |
(7,8,9) |
| 1 | 0.3496 · 0.5441 · 0.8933 |
(19,21,23) |
| 1 | 0.3502 · 0.5435 · 0.8933 |
(2,14,25) |
| 1 | 0.3467 · 0.5476 · 0.8938 |
(20,21,22) |
| 1 | 0.3500 · 0.5449 · 0.8944 |
(3,13,24) |
| 1 | 0.3447 · 0.5502 · 0.8945 |
(0,14,18) |
| 1 | 0.3469 · 0.5509 · 0.8974 |
(1,13,17) |
| 1 | 0.4327 · 0.4881 · 0.9205 |
(4,8,12) |
| 1 | 0.4286 · 0.4942 · 0.9225 |
(9,15,26) |
| 1 | 0.4334 · 0.4921 · 0.9251 |
(7,16,28) |
| 1 | 0.4370 · 0.4901 · 0.9268 |
(10,16,27) |
| 1 | 0.4335 · 0.4966 · 0.9298 |
(17,21,25) |
| 1 | 0.4363 · 0.4943 · 0.9302 |
(18,21,24) |
| 1 | 0.4377 · 0.4934 · 0.9307 |
(3,14,20) |
| 1 | 0.4386 · 0.4944 · 0.9327 |
(2,13,19) |
| 1 | 0.4336 · 0.4999 · 0.9331 |
(1,14,23) |
| 1 | 0.4333 · 0.5002 · 0.9332 |
(5,8,11) |
| 1 | 0.4341 · 0.5004 · 0.9342 |
(0,13,22) |
| 1 | 0.3394 · 0.7065 · 1.0456 |
(9,13,18) |
| 1 | 0.5410 · 0.5429 · 1.0836 |
(8,9,10) |
| 1 | 0.5441 · 0.5476 · 1.0914 |
(19,20,21) |
| 1 | 0.5435 · 0.5502 · 1.0935 |
(0,14,25) |
| 1 | 0.5449 · 0.5509 · 1.0956 |
(1,13,24) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-08-20/convex-n29. - Verified in exact arithmetic: all 3654 triples enumerated, 52 tied at the minimum.
- Friedman's page lists:
A = .006075+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
