Triangle, n = 20 record reconstructed coords
A = 0.011137752662923…
full precision
Exact value of the published coordinate literals:
0.011137752662923215714293869502
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
35 triangles tied (within relative 10−9) at the minimal area, in 35 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1546 · 0.1639 · 0.2738 |
(1,4,9) |
| 1 | 0.1487 · 0.1706 · 0.2748 |
(6,8,10) |
| 1 | 0.1566 · 0.1687 · 0.2854 |
(2,3,7) |
| 1 | 0.1616 · 0.1639 · 0.2858 |
(1,9,14) |
| 1 | 0.1462 · 0.1814 · 0.2881 |
(5,12,16) |
| 1 | 0.1475 · 0.1829 · 0.2926 |
(0,17,18) |
| 1 | 0.1616 · 0.1902 · 0.3235 |
(1,11,14) |
| 1 | 0.1425 · 0.5443 · 0.6820 |
(11,15,19) |
| 1 | 0.2926 · 0.4578 · 0.7480 |
(0,1,17) |
| 1 | 0.2738 · 0.5210 · 0.7926 |
(1,4,13) |
| 1 | 0.2926 · 0.5115 · 0.8020 |
(0,14,17) |
| 1 | 0.1902 · 0.6502 · 0.8380 |
(11,14,18) |
| 1 | 0.1897 · 0.6628 · 0.8502 |
(5,7,19) |
| 1 | 0.1974 · 0.6557 · 0.8508 |
(0,8,13) |
| 1 | 0.3251 · 0.5443 · 0.8678 |
(8,11,19) |
| 1 | 0.2084 · 0.6768 · 0.8832 |
(2,9,13) |
| 1 | 0.2060 · 0.6820 · 0.8860 |
(6,15,19) |
| 1 | 0.3357 · 0.5929 · 0.9272 |
(4,11,16) |
| 1 | 0.3671 · 0.5799 · 0.9457 |
(6,7,12) |
| 1 | 0.3794 · 0.5681 · 0.9462 |
(2,8,17) |
| 1 | 0.4089 · 0.5887 · 0.9965 |
(0,3,9) |
| 1 | 0.3998 · 0.5994 · 0.9982 |
(5,10,15) |
| 1 | 0.3518 · 0.6533 · 1.0041 |
(0,12,19) |
| 1 | 0.3595 · 0.6463 · 1.0048 |
(5,13,17) |
| 1 | 0.3688 · 0.6549 · 1.0227 |
(1,10,19) |
| 1 | 0.3046 · 0.7877 · 1.0913 |
(10,13,18) |
| 1 | 0.2979 · 0.7950 · 1.0919 |
(3,16,19) |
| 1 | 0.2881 · 0.8069 · 1.0941 |
(4,5,12) |
| 1 | 0.2937 · 0.8020 · 1.0948 |
(14,15,17) |
| 1 | 0.2881 · 0.8090 · 1.0962 |
(5,9,12) |
| 1 | 0.2854 · 0.8137 · 1.0981 |
(2,3,12) |
| 1 | 0.2748 · 0.8256 · 1.0993 |
(6,10,17) |
| 1 | 0.3290 · 0.7926 · 1.1207 |
(4,7,13) |
| 1 | 0.2738 · 0.8581 · 1.1310 |
(1,3,4) |
| 1 | 0.2858 · 0.8845 · 1.1695 |
(9,10,14) |
Provenance
- Found by Nathan Sudermann-Merx, August 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 1140 triples enumerated, 35 tied at the minimum.
- Friedman's page lists:
A = .01113+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
