Convex, n = 35 record
A = 0.004056697210914…
full precision
Exact value of the published coordinate literals:
0.00405669721091416695963738304322
Symmetry
Not symmetric (group C1, order 1). The record configuration is listed as: no symmetry.
Minimal triangles
65 triangles tied (within relative 10−9) at the minimal area, in 65 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0570 · 0.2270 · 0.2737 |
(5,9,10) |
| 1 | 0.1286 · 0.1793 · 0.3031 |
(6,20,22) |
| 1 | 0.1218 · 0.2025 · 0.3200 |
(8,15,17) |
| 1 | 0.0570 · 0.2915 · 0.3424 |
(5,9,18) |
| 1 | 0.1679 · 0.1821 · 0.3469 |
(3,7,22) |
| 1 | 0.1588 · 0.2214 · 0.3777 |
(14,30,32) |
| 1 | 0.1643 · 0.2214 · 0.3833 |
(30,31,32) |
| 1 | 0.1286 · 0.3058 · 0.4324 |
(6,7,20) |
| 1 | 0.1183 · 0.3199 · 0.4362 |
(11,16,17) |
| 1 | 0.0990 · 0.3414 · 0.4382 |
(28,29,30) |
| 1 | 0.1679 · 0.2849 · 0.4513 |
(3,7,8) |
| 1 | 0.2265 · 0.2315 · 0.4566 |
(1,3,13) |
| 1 | 0.0735 · 0.4024 · 0.4735 |
(14,28,31) |
| 1 | 0.1819 · 0.3414 · 0.5223 |
(29,30,33) |
| 1 | 0.2030 · 0.3340 · 0.5361 |
(3,11,12) |
| 1 | 0.1414 · 0.4157 · 0.5561 |
(1,22,25) |
| 1 | 0.2256 · 0.3871 · 0.6120 |
(20,21,25) |
| 1 | 0.2559 · 0.3668 · 0.6222 |
(9,17,29) |
| 1 | 0.2782 · 0.3451 · 0.6228 |
(2,7,26) |
| 1 | 0.2080 · 0.4411 · 0.6486 |
(1,4,12) |
| 1 | 0.1999 · 0.4553 · 0.6546 |
(10,24,29) |
| 1 | 0.1859 · 0.5174 · 0.7028 |
(23,24,34) |
| 1 | 0.2068 · 0.5035 · 0.7099 |
(1,11,21) |
| 1 | 0.3030 · 0.4114 · 0.7140 |
(18,19,31) |
| 1 | 0.2641 · 0.4623 · 0.7260 |
(0,3,17) |
| 1 | 0.2858 · 0.4515 · 0.7369 |
(18,24,30) |
| 1 | 0.1729 · 0.6148 · 0.7872 |
(0,13,19) |
| 1 | 0.1196 · 0.6769 · 0.7960 |
(0,10,31) |
| 1 | 0.2884 · 0.5148 · 0.8029 |
(1,6,34) |
| 1 | 0.3507 · 0.4614 · 0.8118 |
(4,5,32) |
| 1 | 0.2668 · 0.5916 · 0.8581 |
(5,28,34) |
| 1 | 0.2849 · 0.5825 · 0.8672 |
(3,8,28) |
| 1 | 0.3115 · 0.5735 · 0.8848 |
(2,11,34) |
| 1 | 0.4331 · 0.4623 · 0.8953 |
(3,17,19) |
| 1 | 0.2878 · 0.6143 · 0.9020 |
(0,1,20) |
| 1 | 0.1718 · 0.7632 · 0.9347 |
(8,18,32) |
| 1 | 0.1295 · 0.8294 · 0.9586 |
(4,8,30) |
| 1 | 0.3236 · 0.6489 · 0.9724 |
(8,29,31) |
| 1 | 0.3050 · 0.7069 · 1.0117 |
(3,15,18) |
| 1 | 0.4692 · 0.5605 · 1.0295 |
(2,10,12) |
| 1 | 0.1859 · 0.8563 · 1.0420 |
(24,31,34) |
| 1 | 0.4974 · 0.5497 · 1.0469 |
(1,16,28) |
| 1 | 0.2602 · 0.8069 · 1.0670 |
(16,20,27) |
| 1 | 0.2907 · 0.7863 · 1.0769 |
(2,5,16) |
| 1 | 0.4336 · 0.6683 · 1.1018 |
(5,15,33) |
| 1 | 0.4793 · 0.6471 · 1.1263 |
(4,13,27) |
| 1 | 0.3505 · 0.7814 · 1.1318 |
(4,6,26) |
| 1 | 0.5753 · 0.6629 · 1.2381 |
(10,25,30) |
| 1 | 0.4093 · 0.8472 · 1.2565 |
(6,12,18) |
| 1 | 0.2394 · 1.0309 · 1.2702 |
(5,6,21) |
| 1 | 0.1348 · 1.1964 · 1.3311 |
(11,25,31) |
| 1 | 0.5287 · 0.8069 · 1.3356 |
(16,20,29) |
| 1 | 0.4547 · 0.9290 · 1.3837 |
(7,15,30) |
| 1 | 0.4212 · 1.0098 · 1.4310 |
(1,18,33) |
| 1 | 0.6477 · 0.8829 · 1.5305 |
(12,21,23) |
| 1 | 0.7469 · 0.7849 · 1.5318 |
(16,22,30) |
| 1 | 0.2602 · 1.3002 · 1.5603 |
(20,27,28) |
| 1 | 0.3495 · 1.2187 · 1.5682 |
(2,13,30) |
| 1 | 0.2827 · 1.2946 · 1.5773 |
(18,20,26) |
| 1 | 0.6218 · 1.0124 · 1.6341 |
(9,14,22) |
| 1 | 0.4472 · 1.2040 · 1.6512 |
(10,21,32) |
| 1 | 0.5689 · 1.1595 · 1.7284 |
(1,26,32) |
| 1 | 0.9143 · 0.9793 · 1.8936 |
(17,27,31) |
| 1 | 0.7159 · 1.2510 · 1.9669 |
(10,27,33) |
| 1 | 0.9667 · 1.0023 · 1.9691 |
(14,17,26) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-08-03/convex-n35. - Verified in exact arithmetic: all 6545 triples enumerated, 65 tied at the minimum.
- Friedman's page lists:
A = .004228+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
