Triangle, n = 32 record
A = 0.004177954667343…
full precision
Exact value of the published coordinate literals:
0.004177954667343989240281118492
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
59 triangles tied (within relative 10−9) at the minimal area, in 59 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0653 · 0.1586 · 0.2040 |
(0,19,27) |
| 1 | 0.1201 · 0.1325 · 0.2431 |
(11,16,26) |
| 1 | 0.1034 · 0.1851 · 0.2817 |
(7,9,23) |
| 1 | 0.1034 · 0.2157 · 0.3139 |
(5,7,9) |
| 1 | 0.1243 · 0.2101 · 0.3302 |
(21,30,31) |
| 1 | 0.2029 · 0.2186 · 0.4196 |
(1,3,4) |
| 1 | 0.1586 · 0.2861 · 0.4430 |
(0,19,28) |
| 1 | 0.2101 · 0.2729 · 0.4817 |
(15,21,30) |
| 1 | 0.1723 · 0.3126 · 0.4836 |
(22,28,30) |
| 1 | 0.2369 · 0.2669 · 0.5027 |
(8,29,31) |
| 1 | 0.2526 · 0.2872 · 0.5389 |
(0,3,29) |
| 1 | 0.1243 · 0.4265 · 0.5495 |
(12,21,31) |
| 1 | 0.1718 · 0.3902 · 0.5611 |
(15,17,31) |
| 1 | 0.1393 · 0.4265 · 0.5648 |
(12,23,31) |
| 1 | 0.1695 · 0.4157 · 0.5844 |
(2,17,22) |
| 1 | 0.2274 · 0.3709 · 0.5976 |
(1,2,6) |
| 1 | 0.2513 · 0.3723 · 0.6229 |
(25,27,29) |
| 1 | 0.2981 · 0.3262 · 0.6237 |
(6,9,29) |
| 1 | 0.2274 · 0.4116 · 0.6385 |
(2,6,23) |
| 1 | 0.2623 · 0.3775 · 0.6392 |
(11,17,30) |
| 1 | 0.1894 · 0.4558 · 0.6445 |
(20,24,30) |
| 1 | 0.1950 · 0.4651 · 0.6595 |
(5,6,31) |
| 1 | 0.2320 · 0.4651 · 0.6967 |
(6,13,31) |
| 1 | 0.1012 · 0.6055 · 0.7058 |
(4,6,28) |
| 1 | 0.2864 · 0.4714 · 0.7575 |
(7,20,21) |
| 1 | 0.3578 · 0.4083 · 0.7658 |
(12,14,15) |
| 1 | 0.2778 · 0.5150 · 0.7925 |
(4,11,22) |
| 1 | 0.2661 · 0.5290 · 0.7949 |
(26,29,30) |
| 1 | 0.1380 · 0.6710 · 0.8085 |
(3,21,25) |
| 1 | 0.3023 · 0.5156 · 0.8176 |
(12,20,22) |
| 1 | 0.2872 · 0.5441 · 0.8310 |
(0,3,6) |
| 1 | 0.1380 · 0.6989 · 0.8364 |
(3,25,31) |
| 1 | 0.3050 · 0.5841 · 0.8888 |
(1,5,27) |
| 1 | 0.1781 · 0.7218 · 0.8995 |
(0,8,20) |
| 1 | 0.2661 · 0.6508 · 0.9167 |
(2,26,30) |
| 1 | 0.2415 · 0.7010 · 0.9423 |
(22,23,24) |
| 1 | 0.4380 · 0.5091 · 0.9469 |
(4,27,30) |
| 1 | 0.3504 · 0.5973 · 0.9475 |
(12,13,16) |
| 1 | 0.3691 · 0.6420 · 1.0110 |
(1,15,29) |
| 1 | 0.2513 · 0.7601 · 1.0112 |
(20,25,27) |
| 1 | 0.3853 · 0.6289 · 1.0141 |
(3,19,20) |
| 1 | 0.3315 · 0.6975 · 1.0289 |
(17,19,21) |
| 1 | 0.3350 · 0.6958 · 1.0307 |
(2,3,10) |
| 1 | 0.4519 · 0.6071 · 1.0589 |
(3,16,30) |
| 1 | 0.4892 · 0.5841 · 1.0732 |
(1,5,14) |
| 1 | 0.3382 · 0.7447 · 1.0827 |
(0,4,13) |
| 1 | 0.1325 · 0.9657 · 1.0980 |
(0,11,26) |
| 1 | 0.1393 · 0.9668 · 1.1059 |
(11,12,23) |
| 1 | 0.3868 · 0.7516 · 1.1382 |
(8,10,22) |
| 1 | 0.3900 · 0.7494 · 1.1393 |
(9,21,26) |
| 1 | 0.2806 · 0.8749 · 1.1554 |
(7,14,25) |
| 1 | 0.1326 · 1.0249 · 1.1573 |
(0,12,24) |
| 1 | 0.2118 · 0.9618 · 1.1735 |
(16,18,29) |
| 1 | 0.5387 · 0.7058 · 1.2444 |
(6,14,28) |
| 1 | 0.4700 · 0.8545 · 1.3244 |
(10,24,26) |
| 1 | 0.4417 · 0.8888 · 1.3305 |
(5,10,27) |
| 1 | 0.4430 · 0.9125 · 1.3554 |
(16,19,28) |
| 1 | 0.4083 · 0.9475 · 1.3557 |
(12,14,16) |
| 1 | 0.5680 · 0.7955 · 1.3634 |
(10,18,19) |
Provenance
- Found by Tej Stead, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-07-25/triangle-n32. - Verified in exact arithmetic: all 4960 triples enumerated, 59 tied at the minimum.
- Friedman's page lists:
A = .004177+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
