Triangle, n = 21 record
A = 0.010622865539885…
full precision
Exact value of the published coordinate literals:
0.010622865539885889003407639544
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
37 triangles tied (within relative 10−9) at the minimal area, in 37 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1591 · 0.1649 · 0.2887 |
(0,2,4) |
| 1 | 0.1607 · 0.1677 · 0.2952 |
(8,10,14) |
| 1 | 0.1582 · 0.1704 · 0.2954 |
(9,11,15) |
| 1 | 0.1610 · 0.1689 · 0.2972 |
(16,18,19) |
| 1 | 0.1593 · 0.1717 · 0.2989 |
(1,3,5) |
| 1 | 0.1689 · 0.1850 · 0.3295 |
(14,18,19) |
| 1 | 0.1717 · 0.1822 · 0.3296 |
(0,1,3) |
| 1 | 0.1732 · 0.1912 · 0.3426 |
(9,13,17) |
| 1 | 0.1593 · 0.3923 · 0.5448 |
(3,5,7) |
| 1 | 0.1704 · 0.3919 · 0.5560 |
(7,9,11) |
| 1 | 0.1610 · 0.4107 · 0.5654 |
(7,16,19) |
| 1 | 0.1591 · 0.4167 · 0.5697 |
(2,4,7) |
| 1 | 0.1582 · 0.4224 · 0.5746 |
(7,17,20) |
| 1 | 0.1607 · 0.4246 · 0.5795 |
(7,8,10) |
| 1 | 0.2989 · 0.4424 · 0.7389 |
(1,5,9) |
| 1 | 0.3923 · 0.4107 · 0.8012 |
(5,7,16) |
| 1 | 0.4167 · 0.4224 · 0.8375 |
(4,7,17) |
| 1 | 0.1610 · 0.6912 · 0.8497 |
(9,16,19) |
| 1 | 0.1607 · 0.7058 · 0.8642 |
(5,8,10) |
| 1 | 0.1582 · 0.7417 · 0.8977 |
(8,17,20) |
| 1 | 0.3526 · 0.6090 · 0.9605 |
(15,17,19) |
| 1 | 0.3792 · 0.5844 · 0.9625 |
(1,4,10) |
| 1 | 0.3864 · 0.5814 · 0.9667 |
(2,8,18) |
| 1 | 0.4059 · 0.5873 · 0.9922 |
(0,5,11) |
| 1 | 0.4049 · 0.6094 · 1.0134 |
(14,16,20) |
| 1 | 0.3614 · 0.6612 · 1.0217 |
(5,12,18) |
| 1 | 0.3740 · 0.6603 · 1.0334 |
(9,12,14) |
| 1 | 0.2972 · 0.8195 · 1.1159 |
(15,16,18) |
| 1 | 0.2952 · 0.8220 · 1.1164 |
(1,8,14) |
| 1 | 0.2887 · 0.8289 · 1.1167 |
(0,4,18) |
| 1 | 0.3220 · 0.8034 · 1.1247 |
(2,6,15) |
| 1 | 0.2954 · 0.8408 · 1.1354 |
(0,9,15) |
| 1 | 0.3071 · 0.8472 · 1.1535 |
(1,12,19) |
| 1 | 0.2987 · 0.8559 · 1.1538 |
(3,6,18) |
| 1 | 0.3202 · 0.8531 · 1.1726 |
(10,12,15) |
| 1 | 0.2858 · 0.8917 · 1.1768 |
(11,13,14) |
| 1 | 0.3028 · 0.8798 · 1.1818 |
(0,13,20) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-08-20/triangle-n21. - Verified in exact arithmetic: all 1330 triples enumerated, 37 tied at the minimum.
- Friedman's page lists:
A = .01056+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
