Convex, n = 32 record
A = 0.004886721759223…
full precision
Exact value of the published coordinate literals:
0.00488672175922345706877878551714
Symmetry
Not symmetric (group C1, order 1). The record configuration is listed as: 8-fold dihedral symmetry.
Minimal triangles
59 triangles tied (within relative 10−9) at the minimal area, in 59 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0622 · 0.1577 · 0.1748 |
(14,30,31) |
| 1 | 0.1003 · 0.1270 · 0.2062 |
(2,6,22) |
| 1 | 0.0800 · 0.1643 · 0.2257 |
(21,26,27) |
| 1 | 0.1373 · 0.2062 · 0.3384 |
(6,20,22) |
| 1 | 0.1355 · 0.2260 · 0.3571 |
(8,15,17) |
| 1 | 0.0638 · 0.3086 · 0.3654 |
(5,9,18) |
| 1 | 0.1816 · 0.1983 · 0.3763 |
(3,7,22) |
| 1 | 0.0638 · 0.3920 · 0.4515 |
(5,9,19) |
| 1 | 0.1031 · 0.3630 · 0.4633 |
(28,29,30) |
| 1 | 0.1373 · 0.3392 · 0.4743 |
(6,7,20) |
| 1 | 0.0622 · 0.4172 · 0.4754 |
(14,28,31) |
| 1 | 0.1816 · 0.3066 · 0.4864 |
(3,7,8) |
| 1 | 0.1721 · 0.3306 · 0.5010 |
(10,15,16) |
| 1 | 0.2464 · 0.2608 · 0.5057 |
(1,3,13) |
| 1 | 0.2608 · 0.3715 · 0.6315 |
(3,13,25) |
| 1 | 0.2381 · 0.3996 · 0.6369 |
(20,21,25) |
| 1 | 0.2899 · 0.3495 · 0.6387 |
(0,5,28) |
| 1 | 0.3208 · 0.3441 · 0.6642 |
(4,9,23) |
| 1 | 0.1672 · 0.4993 · 0.6657 |
(4,10,19) |
| 1 | 0.2149 · 0.4658 · 0.6800 |
(2,3,21) |
| 1 | 0.2219 · 0.4818 · 0.7030 |
(1,4,12) |
| 1 | 0.2087 · 0.5282 · 0.7363 |
(1,11,21) |
| 1 | 0.2180 · 0.5309 · 0.7483 |
(10,24,28) |
| 1 | 0.3200 · 0.4314 · 0.7509 |
(18,19,31) |
| 1 | 0.2977 · 0.4845 · 0.7817 |
(18,24,30) |
| 1 | 0.2737 · 0.5087 · 0.7820 |
(0,3,17) |
| 1 | 0.2956 · 0.5049 · 0.8001 |
(5,8,23) |
| 1 | 0.1201 · 0.7144 · 0.8339 |
(0,10,31) |
| 1 | 0.1832 · 0.6517 · 0.8345 |
(0,13,19) |
| 1 | 0.1403 · 0.7182 · 0.8579 |
(5,11,25) |
| 1 | 0.3066 · 0.6126 · 0.9189 |
(3,8,28) |
| 1 | 0.2681 · 0.6572 · 0.9251 |
(9,12,29) |
| 1 | 0.4426 · 0.5058 · 0.9482 |
(11,20,24) |
| 1 | 0.3017 · 0.6484 · 0.9498 |
(0,1,20) |
| 1 | 0.4526 · 0.5087 · 0.9611 |
(3,17,19) |
| 1 | 0.2450 · 0.7182 · 0.9629 |
(6,17,21) |
| 1 | 0.1400 · 0.8664 · 1.0060 |
(4,8,30) |
| 1 | 0.3312 · 0.7442 · 1.0752 |
(3,15,18) |
| 1 | 0.4998 · 0.5852 · 1.0849 |
(2,10,12) |
| 1 | 0.4778 · 0.6194 · 1.0971 |
(4,7,28) |
| 1 | 0.5266 · 0.5880 · 1.1145 |
(1,16,28) |
| 1 | 0.2681 · 0.8666 · 1.1345 |
(1,9,29) |
| 1 | 0.2963 · 0.8560 · 1.1521 |
(16,20,27) |
| 1 | 0.5184 · 0.7057 · 1.2240 |
(4,13,27) |
| 1 | 0.5506 · 0.7465 · 1.2971 |
(3,9,30) |
| 1 | 0.6072 · 0.7021 · 1.3093 |
(10,25,30) |
| 1 | 0.4351 · 0.8917 · 1.3267 |
(6,12,18) |
| 1 | 0.4661 · 0.8682 · 1.3342 |
(13,16,31) |
| 1 | 0.6248 · 0.7103 · 1.3349 |
(2,15,28) |
| 1 | 0.1403 · 1.2668 · 1.4069 |
(11,25,31) |
| 1 | 0.5531 · 0.8560 · 1.4090 |
(16,20,29) |
| 1 | 0.4920 · 0.9703 · 1.4622 |
(7,15,30) |
| 1 | 0.5699 · 1.0144 · 1.5842 |
(13,21,29) |
| 1 | 0.8032 · 0.8184 · 1.6216 |
(16,22,30) |
| 1 | 0.3716 · 1.2800 · 1.6515 |
(2,13,30) |
| 1 | 0.2963 · 1.3782 · 1.6744 |
(20,27,28) |
| 1 | 0.3000 · 1.3968 · 1.6968 |
(20,23,26) |
| 1 | 0.6288 · 1.0797 · 1.7084 |
(9,14,22) |
| 1 | 0.9489 · 1.0614 · 2.0102 |
(17,27,31) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-07-25/convex-n32. - Verified in exact arithmetic: all 4960 triples enumerated, 59 tied at the minimum.
- Friedman's page lists:
A = .004933+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
