Square, n = 29 record
A = 0.006275939213171…
full precision
Exact value of the published coordinate literals:
0.00627593921317175235788970901259
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
51 triangles tied (within relative 10−9) at the minimal area, in 51 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1513 · 0.1553 · 0.2946 |
(1,20,25) |
| 1 | 0.1515 · 0.1557 · 0.2952 |
(6,21,26) |
| 1 | 0.1549 · 0.1564 · 0.2998 |
(4,7,9) |
| 1 | 0.1552 · 0.1566 · 0.3004 |
(2,12,22) |
| 1 | 0.1421 · 0.1705 · 0.3012 |
(3,10,18) |
| 1 | 0.1423 · 0.1709 · 0.3018 |
(15,17,28) |
| 1 | 0.1278 · 0.3392 · 0.4630 |
(13,19,27) |
| 1 | 0.2650 · 0.3569 · 0.6206 |
(17,20,24) |
| 1 | 0.2652 · 0.3570 · 0.6208 |
(5,18,26) |
| 1 | 0.1553 · 0.4920 · 0.6457 |
(0,20,25) |
| 1 | 0.1557 · 0.4930 · 0.6471 |
(14,21,26) |
| 1 | 0.1705 · 0.4839 · 0.6529 |
(2,10,18) |
| 1 | 0.1709 · 0.4849 · 0.6543 |
(4,15,17) |
| 1 | 0.1549 · 0.5064 · 0.6597 |
(6,7,9) |
| 1 | 0.1552 · 0.5074 · 0.6610 |
(1,12,22) |
| 1 | 0.3780 · 0.3859 · 0.7632 |
(2,3,13) |
| 1 | 0.3784 · 0.3864 · 0.7641 |
(4,11,28) |
| 1 | 0.3706 · 0.4004 · 0.7703 |
(4,6,25) |
| 1 | 0.3709 · 0.4008 · 0.7710 |
(1,2,21) |
| 1 | 0.3629 · 0.4096 · 0.7718 |
(10,14,28) |
| 1 | 0.3632 · 0.4101 · 0.7725 |
(0,3,15) |
| 1 | 0.3146 · 0.4920 · 0.8060 |
(0,20,27) |
| 1 | 0.3107 · 0.4969 · 0.8070 |
(10,12,26) |
| 1 | 0.3152 · 0.4930 · 0.8076 |
(14,26,27) |
| 1 | 0.3111 · 0.4974 · 0.8078 |
(9,15,20) |
| 1 | 0.3270 · 0.4872 · 0.8136 |
(11,17,25) |
| 1 | 0.3272 · 0.4877 · 0.8143 |
(13,18,21) |
| 1 | 0.3218 · 0.5094 · 0.8306 |
(9,21,22) |
| 1 | 0.3221 · 0.5099 · 0.8314 |
(7,12,25) |
| 1 | 0.1421 · 0.7217 · 0.8629 |
(3,18,20) |
| 1 | 0.1423 · 0.7230 · 0.8644 |
(17,26,28) |
| 1 | 0.1617 · 0.7047 · 0.8656 |
(7,14,23) |
| 1 | 0.1619 · 0.7060 · 0.8671 |
(0,8,22) |
| 1 | 0.3473 · 0.5290 · 0.8758 |
(1,8,9) |
| 1 | 0.3475 · 0.5293 · 0.8763 |
(6,12,23) |
| 1 | 0.2546 · 0.6252 · 0.8792 |
(6,19,22) |
| 1 | 0.3629 · 0.5336 · 0.8960 |
(10,14,17) |
| 1 | 0.3632 · 0.5339 · 0.8966 |
(0,15,18) |
| 1 | 0.3706 · 0.5356 · 0.9058 |
(4,25,26) |
| 1 | 0.3709 · 0.5358 · 0.9063 |
(2,20,21) |
| 1 | 0.1549 · 0.8030 · 0.9572 |
(7,9,18) |
| 1 | 0.4646 · 0.4946 · 0.9588 |
(25,27,28) |
| 1 | 0.1552 · 0.8048 · 0.9594 |
(12,17,22) |
| 1 | 0.4655 · 0.4955 · 0.9607 |
(3,21,27) |
| 1 | 0.1553 · 0.8271 · 0.9818 |
(20,23,25) |
| 1 | 0.1557 · 0.8290 · 0.9840 |
(8,21,26) |
| 1 | 0.1750 · 0.8271 · 1.0016 |
(13,20,23) |
| 1 | 0.1754 · 0.8290 · 1.0038 |
(8,11,26) |
| 1 | 0.3152 · 0.7454 · 1.0603 |
(5,14,27) |
| 1 | 0.2946 · 0.8719 · 1.1662 |
(1,10,25) |
| 1 | 0.2952 · 0.8736 · 1.1685 |
(6,15,21) |
Provenance
- Found by Rhys Chappell, September 2026.
- Coordinates by an external contributor, re-verified here:
autoheilbronn v4 topology/annealing campaign; exact rational verification— Line-arrangement-guided insertion and stress-weighted ruin/recreate, followed by filtered trust-region SLP polishing; GPU annealing was also used where recorded in the result provenance.. - Verified in exact arithmetic: all 3654 triples enumerated, 51 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
