Square, n = 19 record reconstructed coords
A = 0.013386177617368…
full precision
Exact value of the published coordinate literals:
0.0133861776173687205577346807455
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
32 triangles tied (within relative 10−9) at the minimal area, in 32 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1612 · 0.2304 · 0.3612 |
(13,16,17) |
| 1 | 0.1660 · 0.2349 · 0.3734 |
(1,5,14) |
| 1 | 0.1649 · 0.2364 · 0.3739 |
(0,3,15) |
| 1 | 0.2488 · 0.2545 · 0.4913 |
(3,4,12) |
| 1 | 0.2442 · 0.2592 · 0.4914 |
(2,5,10) |
| 1 | 0.2480 · 0.2592 · 0.4955 |
(2,4,11) |
| 1 | 0.2562 · 0.2834 · 0.5300 |
(1,9,11) |
| 1 | 0.2592 · 0.3909 · 0.6446 |
(2,4,9) |
| 1 | 0.2592 · 0.4139 · 0.6680 |
(2,10,18) |
| 1 | 0.2605 · 0.4233 · 0.6790 |
(8,10,12) |
| 1 | 0.2699 · 0.4714 · 0.7374 |
(0,8,17) |
| 1 | 0.2582 · 0.4922 · 0.7466 |
(6,7,15) |
| 1 | 0.2818 · 0.4769 · 0.7551 |
(13,14,18) |
| 1 | 0.2750 · 0.4845 · 0.7559 |
(8,16,18) |
| 1 | 0.2865 · 0.4905 · 0.7737 |
(3,6,8) |
| 1 | 0.3690 · 0.4104 · 0.7763 |
(2,12,17) |
| 1 | 0.2304 · 0.6010 · 0.8282 |
(3,16,17) |
| 1 | 0.2364 · 0.5959 · 0.8293 |
(3,11,15) |
| 1 | 0.2349 · 0.6039 · 0.8358 |
(5,14,16) |
| 1 | 0.3612 · 0.5246 · 0.8836 |
(0,13,16) |
| 1 | 0.3567 · 0.5300 · 0.8846 |
(1,7,11) |
| 1 | 0.3739 · 0.5261 · 0.8980 |
(0,3,7) |
| 1 | 0.3734 · 0.5362 · 0.9076 |
(1,5,13) |
| 1 | 0.4410 · 0.4955 · 0.9348 |
(4,8,11) |
| 1 | 0.3567 · 0.6002 · 0.9551 |
(7,11,14) |
| 1 | 0.3612 · 0.5962 · 0.9556 |
(13,15,16) |
| 1 | 0.3734 · 0.6092 · 0.9810 |
(1,5,17) |
| 1 | 0.3909 · 0.6379 · 1.0274 |
(2,9,15) |
| 1 | 0.4614 · 0.6680 · 1.1284 |
(2,7,18) |
| 1 | 0.4666 · 0.6747 · 1.1404 |
(6,12,13) |
| 1 | 0.4707 · 0.6790 · 1.1486 |
(1,8,10) |
| 1 | 0.4078 · 0.7618 · 1.1687 |
(4,14,15) |
Provenance
- Found by William Shanley, July 2026.
- Coordinates reconstructed by local optimization:
heilbronn-site reconstruct/reconstruct.py— re-polished from the published record figure — the record holder's arrangement with re-derived coordinates. - Verified in exact arithmetic: all 969 triples enumerated, 32 tied at the minimum.
- Friedman's page lists:
A = 0.01338+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
