Convex, n = 27 record
A = 0.008029121778491…
full precision
Exact value of the published coordinate literals:
0.00802912177849179439287760586858
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
48 triangles tied (within relative 10−9) at the minimal area, in 48 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1600 · 0.1985 · 0.3546 |
(13,18,24) |
| 1 | 0.1561 · 0.2065 · 0.3589 |
(11,21,22) |
| 1 | 0.1665 · 0.1998 · 0.3628 |
(10,19,26) |
| 1 | 0.1561 · 0.2104 · 0.3629 |
(11,20,22) |
| 1 | 0.1654 · 0.2031 · 0.3650 |
(9,19,25) |
| 1 | 0.1698 · 0.2062 · 0.3727 |
(12,18,23) |
| 1 | 0.1665 · 0.2135 · 0.3768 |
(10,20,26) |
| 1 | 0.1698 · 0.2140 · 0.3807 |
(12,21,23) |
| 1 | 0.1389 · 0.2599 · 0.3958 |
(7,9,13) |
| 1 | 0.1392 · 0.2636 · 0.3999 |
(4,10,11) |
| 1 | 0.1425 · 0.2628 · 0.4025 |
(7,24,25) |
| 1 | 0.1390 · 0.2672 · 0.4033 |
(6,12,13) |
| 1 | 0.1381 · 0.2700 · 0.4052 |
(8,25,26) |
| 1 | 0.1434 · 0.2729 · 0.4137 |
(5,22,23) |
| 1 | 0.1362 · 0.2986 · 0.4323 |
(6,7,23) |
| 1 | 0.1389 · 0.2986 · 0.4351 |
(6,7,9) |
| 1 | 0.1381 · 0.3092 · 0.4450 |
(4,8,25) |
| 1 | 0.1392 · 0.3092 · 0.4462 |
(4,8,11) |
| 1 | 0.1409 · 0.3086 · 0.4473 |
(7,8,10) |
| 1 | 0.1425 · 0.3086 · 0.4490 |
(7,8,24) |
| 1 | 0.1390 · 0.3155 · 0.4523 |
(5,6,13) |
| 1 | 0.1434 · 0.3155 · 0.4569 |
(5,6,22) |
| 1 | 0.2268 · 0.2546 · 0.4799 |
(11,14,26) |
| 1 | 0.2333 · 0.2632 · 0.4951 |
(1,12,22) |
| 1 | 0.1985 · 0.3958 · 0.5934 |
(9,13,18) |
| 1 | 0.2065 · 0.3905 · 0.5961 |
(21,22,26) |
| 1 | 0.1998 · 0.3999 · 0.5988 |
(10,11,19) |
| 1 | 0.2031 · 0.4025 · 0.6047 |
(19,24,25) |
| 1 | 0.2104 · 0.4003 · 0.6099 |
(11,12,20) |
| 1 | 0.2140 · 0.4033 · 0.6165 |
(12,13,21) |
| 1 | 0.2135 · 0.4052 · 0.6179 |
(20,25,26) |
| 1 | 0.2062 · 0.4137 · 0.6191 |
(18,22,23) |
| 1 | 0.1110 · 0.6333 · 0.7435 |
(16,23,25) |
| 1 | 0.1113 · 0.6365 · 0.7470 |
(0,10,12) |
| 1 | 0.1132 · 0.6402 · 0.7526 |
(2,9,12) |
| 1 | 0.1154 · 0.6410 · 0.7556 |
(14,22,25) |
| 1 | 0.1122 · 0.6473 · 0.7588 |
(15,23,26) |
| 1 | 0.1144 · 0.6488 · 0.7624 |
(3,10,13) |
| 1 | 0.1110 · 0.6659 · 0.7762 |
(12,16,25) |
| 1 | 0.1132 · 0.6659 · 0.7784 |
(2,12,25) |
| 1 | 0.1184 · 0.6609 · 0.7786 |
(1,11,13) |
| 1 | 0.1172 · 0.6623 · 0.7788 |
(17,24,26) |
| 1 | 0.1113 · 0.6709 · 0.7814 |
(0,10,23) |
| 1 | 0.1122 · 0.6709 · 0.7824 |
(10,15,23) |
| 1 | 0.1154 · 0.6814 · 0.7961 |
(9,14,22) |
| 1 | 0.1144 · 0.6883 · 0.8020 |
(3,13,26) |
| 1 | 0.1172 · 0.6883 · 0.8049 |
(13,17,26) |
| 1 | 0.1184 · 0.6951 · 0.8128 |
(1,11,24) |
Provenance
- Found by Fable 5.1 with Shengtong Zhang, September 2026.
- Coordinates by an external contributor, re-verified here:
Fable51 search campaign, September 2026: symmetry-reduced basin hopping (orbit parametrization, greedy ruin-and-recreate, soft-min warm-up, trust-region SLP) and insertion ladders from neighbouring records; tie system refined to 80 digits by damped Gauss-Newton; verified in exact rational arithmetic— not symmetric; 48 tied minimal triangles. - Verified in exact arithmetic: all 2925 triples enumerated, 48 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
