Triangle, n = 20 record
A = 0.012609391528641…
full precision
Exact value of the published coordinate literals:
0.0126093915286413226018464017698
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 | 0.1429 · 0.2369 · 0.3488 |
(9,14,19) |
| 1 | 0.1182 · 0.2671 · 0.3513 |
(12,15,17) |
| 1 | 0.1182 · 0.2689 · 0.3536 |
(12,15,18) |
| 1 | 0.1429 · 0.2970 · 0.4205 |
(4,9,14) |
| 1 | 0.1625 · 0.2828 · 0.4281 |
(10,13,16) |
| 1 | 0.2212 · 0.2518 · 0.4600 |
(5,10,11) |
| 1 | 0.2183 · 0.3053 · 0.5141 |
(2,3,19) |
| 1 | 0.2483 · 0.2852 · 0.5247 |
(1,2,6) |
| 1 | 0.2501 · 0.3146 · 0.5574 |
(3,5,17) |
| 1 | 0.2535 · 0.3174 · 0.5638 |
(1,8,18) |
| 1 | 0.2369 · 0.3965 · 0.6279 |
(6,9,19) |
| 1 | 0.2671 · 0.4391 · 0.7023 |
(10,15,17) |
| 1 | 0.2689 · 0.4474 · 0.7126 |
(4,12,18) |
| 1 | 0.2970 · 0.4474 · 0.7411 |
(4,14,18) |
| 1 | 0.2855 · 0.4600 · 0.7423 |
(10,11,18) |
| 1 | 0.2867 · 0.4692 · 0.7527 |
(4,11,17) |
| 1 | 0.3452 · 0.4274 · 0.7699 |
(2,7,16) |
| 1 | 0.2852 · 0.5141 · 0.7966 |
(3,10,19) |
| 1 | 0.2765 · 0.5247 · 0.7985 |
(1,4,6) |
| 1 | 0.4131 · 0.4274 · 0.8383 |
(2,9,16) |
| 1 | 0.3965 · 0.5546 · 0.9496 |
(0,6,19) |
| 1 | 0.2855 · 0.6781 · 0.9619 |
(11,13,18) |
| 1 | 0.4806 · 0.4968 · 0.9760 |
(5,13,15) |
| 1 | 0.2867 · 0.7056 · 0.9907 |
(11,14,17) |
| 1 | 0.4996 · 0.5036 · 1.0019 |
(8,12,14) |
| 1 | 0.4806 · 0.5510 · 1.0304 |
(5,12,13) |
| 1 | 0.3426 · 0.7867 · 1.1282 |
(1,12,19) |
| 1 | 0.3798 · 0.7749 · 1.1538 |
(3,6,15) |
| 1 | 0.5145 · 0.6756 · 1.1893 |
(3,7,8) |
| 1 | 0.5310 · 0.6837 · 1.2140 |
(0,1,5) |
| 1 | 0.4770 · 0.7699 · 1.2462 |
(2,7,14) |
| 1 | 0.4998 · 0.7549 · 1.2541 |
(0,2,13) |
| 1 | 0.3627 · 0.9619 · 1.3239 |
(7,13,18) |
| 1 | 0.3641 · 0.9907 · 1.3541 |
(0,14,17) |
| 1 | 0.5554 · 0.9496 · 1.5046 |
(0,6,7) |
Provenance
- Found by Rob Gardiner, September 2026.
- Coordinates by an external contributor, re-verified here:
Rob Gardiner, Heilbronn triangle configurations, September 2026.— Search from random starting configurations. - Verified in exact arithmetic: all 1140 triples enumerated, 35 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
