Square, n = 30 record
A = 0.006038527494905…
full precision
Exact value of the published coordinate literals:
0.0060385274949059229725757188645
Symmetry
Symmetry
180° Rotationally symmetric (group C2, order 2).
30 points in 15 orbits (2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2) — hover a point to see its orbit.
Minimal triangles
54 triangles tied (within relative 10−9) at the minimal area, in 27 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 2 | 0.2082 · 0.3635 · 0.5700 |
(6,12,17) (7,13,16) |
| 2 | 0.2125 · 0.3788 · 0.5898 |
(1,11,18) (2,8,19) |
| 2 | 0.2133 · 0.3796 · 0.5914 |
(0,10,20) (3,9,21) |
| 2 | 0.2056 · 0.3887 · 0.5927 |
(0,14,29) (3,15,26) |
| 2 | 0.2120 · 0.3994 · 0.6099 |
(4,10,29) (5,9,26) |
| 2 | 0.2123 · 0.3994 · 0.6103 |
(1,22,24) (2,23,25) |
| 2 | 0.2135 · 0.4029 · 0.6149 |
(1,12,28) (2,13,27) |
| 2 | 0.2183 · 0.4192 · 0.6362 |
(6,11,28) (7,8,27) |
| 2 | 0.2082 · 0.4814 · 0.6885 |
(4,6,17) (5,7,16) |
| 2 | 0.2125 · 0.4978 · 0.7093 |
(0,2,19) (1,3,18) |
| 2 | 0.2451 · 0.4919 · 0.7362 |
(9,22,27) (10,23,28) |
| 2 | 0.3635 · 0.3798 · 0.7426 |
(0,6,12) (3,7,13) |
| 2 | 0.3568 · 0.3887 · 0.7448 |
(14,17,29) (15,16,26) |
| 2 | 0.2499 · 0.4999 · 0.7490 |
(14,25,27) (15,24,28) |
| 2 | 0.3788 · 0.3849 · 0.7630 |
(1,5,11) (2,4,8) |
| 2 | 0.3646 · 0.3994 · 0.7633 |
(9,18,26) (10,19,29) |
| 2 | 0.3699 · 0.4008 · 0.7701 |
(1,4,14) (2,5,15) |
| 2 | 0.2561 · 0.5200 · 0.7754 |
(8,23,26) (11,22,29) |
| 2 | 0.3658 · 0.4192 · 0.7844 |
(8,20,27) (11,21,28) |
| 2 | 0.3841 · 0.4848 · 0.8684 |
(0,9,25) (3,10,24) |
| 2 | 0.3938 · 0.6149 · 1.0084 |
(1,12,20) (2,13,21) |
| 2 | 0.4100 · 0.6099 · 1.0197 |
(4,10,16) (5,9,17) |
| 2 | 0.4557 · 0.5663 · 1.0217 |
(14,19,23) (15,18,22) |
| 2 | 0.4867 · 0.5852 · 1.0717 |
(12,21,22) (13,20,23) |
| 2 | 0.5622 · 0.6103 · 1.1723 |
(1,16,24) (2,17,25) |
| 2 | 0.5663 · 0.6130 · 1.1791 |
(6,19,23) (7,18,22) |
| 2 | 0.5852 · 0.6477 · 1.2327 |
(4,21,22) (5,20,23) |
Provenance
- Found by Tej Stead, September 2026.
- Coordinates by an external contributor, re-verified here:
heilbronn-site search/refine.py — square n=31 record minus one point, re-polished— The n=31 configuration (Coupvent des Graviers' n=32 minus one point) with one more point deleted and re-polished; the ladder stops here, as one further deletion falls 2.6% short of the n=29 record.. - Verified in exact arithmetic: all 4060 triples enumerated, 54 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
