Convex, n = 33 record
A = 0.005470136067289…
full precision
Exact value of the published coordinate literals:
0.00547013606728989452109453373057
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
61 triangles tied (within relative 10−9) at the minimal area, in 61 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1169 · 0.1203 · 0.2139 |
(0,20,30) |
| 1 | 0.1143 · 0.1231 · 0.2142 |
(3,23,29) |
| 1 | 0.1171 · 0.1238 · 0.2193 |
(2,22,28) |
| 1 | 0.0977 · 0.3355 · 0.4289 |
(1,13,15) |
| 1 | 0.0977 · 0.3385 · 0.4320 |
(3,13,15) |
| 1 | 0.1172 · 0.3281 · 0.4418 |
(2,12,14) |
| 1 | 0.1204 · 0.3355 · 0.4526 |
(1,15,21) |
| 1 | 0.1364 · 0.3428 · 0.4765 |
(5,11,17) |
| 1 | 0.1203 · 0.3653 · 0.4827 |
(0,16,30) |
| 1 | 0.1231 · 0.3649 · 0.4852 |
(3,19,29) |
| 1 | 0.1238 · 0.3664 · 0.4875 |
(2,18,28) |
| 1 | 0.1267 · 0.3637 · 0.4877 |
(1,17,31) |
| 1 | 0.1594 · 0.3488 · 0.5061 |
(4,10,16) |
| 1 | 0.1636 · 0.3621 · 0.5238 |
(8,17,26) |
| 1 | 0.1686 · 0.3622 · 0.5290 |
(11,18,25) |
| 1 | 0.2680 · 0.2688 · 0.5352 |
(25,26,29) |
| 1 | 0.1664 · 0.3735 · 0.5380 |
(9,16,27) |
| 1 | 0.2679 · 0.2737 · 0.5401 |
(24,27,31) |
| 1 | 0.2680 · 0.2756 · 0.5422 |
(25,26,30) |
| 1 | 0.2737 · 0.2774 · 0.5497 |
(24,27,28) |
| 1 | 0.1636 · 0.4030 · 0.5650 |
(6,17,26) |
| 1 | 0.1686 · 0.4038 · 0.5708 |
(5,18,25) |
| 1 | 0.1664 · 0.4180 · 0.5829 |
(7,16,27) |
| 1 | 0.2142 · 0.4088 · 0.6219 |
(11,24,26) |
| 1 | 0.2138 · 0.4101 · 0.6228 |
(8,25,27) |
| 1 | 0.2227 · 0.4088 · 0.6304 |
(9,24,26) |
| 1 | 0.3100 · 0.3809 · 0.6902 |
(17,23,24) |
| 1 | 0.2922 · 0.4418 · 0.7333 |
(2,14,32) |
| 1 | 0.2943 · 0.4701 · 0.7638 |
(4,21,32) |
| 1 | 0.1969 · 0.5835 · 0.7797 |
(3,8,20) |
| 1 | 0.1917 · 0.5905 · 0.7815 |
(0,11,23) |
| 1 | 0.2019 · 0.5983 · 0.7996 |
(1,10,22) |
| 1 | 0.1978 · 0.6034 · 0.8006 |
(9,21,28) |
| 1 | 0.1267 · 0.6982 · 0.8241 |
(1,23,31) |
| 1 | 0.1203 · 0.7080 · 0.8274 |
(0,22,30) |
| 1 | 0.3621 · 0.4767 · 0.8384 |
(8,15,26) |
| 1 | 0.3759 · 0.4722 · 0.8478 |
(10,13,24) |
| 1 | 0.1618 · 0.6866 · 0.8477 |
(19,24,32) |
| 1 | 0.3622 · 0.4928 · 0.8546 |
(11,12,25) |
| 1 | 0.2943 · 0.5645 · 0.8584 |
(1,4,32) |
| 1 | 0.3488 · 0.5474 · 0.8959 |
(10,16,20) |
| 1 | 0.3484 · 0.5488 · 0.8969 |
(9,19,23) |
| 1 | 0.3464 · 0.5563 · 0.9024 |
(8,18,22) |
| 1 | 0.3428 · 0.5631 · 0.9056 |
(11,17,21) |
| 1 | 0.4030 · 0.5217 · 0.9244 |
(6,26,31) |
| 1 | 0.4038 · 0.5295 · 0.9330 |
(5,25,28) |
| 1 | 0.4343 · 0.5207 · 0.9547 |
(4,24,29) |
| 1 | 0.2688 · 0.7069 · 0.9753 |
(14,26,29) |
| 1 | 0.4090 · 0.6106 · 1.0194 |
(0,28,32) |
| 1 | 0.2195 · 0.8074 · 1.0266 |
(19,20,31) |
| 1 | 0.3809 · 0.6509 · 1.0315 |
(7,17,23) |
| 1 | 0.2265 · 0.8058 · 1.0320 |
(16,23,28) |
| 1 | 0.3953 · 0.6426 · 1.0377 |
(5,19,21) |
| 1 | 0.3930 · 0.6449 · 1.0377 |
(6,16,22) |
| 1 | 0.3207 · 0.7303 · 1.0508 |
(0,15,17) |
| 1 | 0.3837 · 0.6681 · 1.0516 |
(4,18,20) |
| 1 | 0.3181 · 0.7404 · 1.0582 |
(2,13,19) |
| 1 | 0.3315 · 0.7299 · 1.0612 |
(3,12,18) |
| 1 | 0.3371 · 0.7355 · 1.0724 |
(1,14,16) |
| 1 | 0.1938 · 0.9140 · 1.1075 |
(20,22,32) |
| 1 | 0.5837 · 0.6449 · 1.2285 |
(6,16,32) |
Provenance
- Found by Alexandar Lackovic with help of Opus 5.5, September 2026.
- Coordinates by an external contributor, re-verified here:
Basin hopping search (with best spot reinsertion and shake moves, elite pool, laddered/symmetric seeds) with SLSQP polishing of the max-min-area problem. Originally implemented by Alexandar Lackovic in Python, then optimized and ported to C++ by Opus 5.5. https://github.com/codrAlex/heilbronn-search— Not symmetric. Found by basin hopping with best spot reinsertion moves and SLSQP polishing of the max-min-area problem. - Verified in exact arithmetic: all 5456 triples enumerated, 61 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
