Convex, n = 25 record
A = 0.009316105977690…
full precision
Exact value of the published coordinate literals:
0.00931610597769021064542063737195
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
45 triangles tied (within relative 10−9) at the minimal area, in 45 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.0816 · 0.4304 · 0.5014 |
(8,23,24) |
| 1 | 0.1928 · 0.4366 · 0.6260 |
(12,13,24) |
| 1 | 0.3016 · 0.3307 · 0.6295 |
(7,18,24) |
| 1 | 0.3154 · 0.3536 · 0.6667 |
(2,13,17) |
| 1 | 0.1900 · 0.4799 · 0.6671 |
(16,20,22) |
| 1 | 0.2534 · 0.4338 · 0.6849 |
(1,11,17) |
| 1 | 0.3282 · 0.3624 · 0.6885 |
(0,9,20) |
| 1 | 0.2615 · 0.4543 · 0.7137 |
(4,8,9) |
| 1 | 0.2615 · 0.4591 · 0.7186 |
(4,9,10) |
| 1 | 0.2769 · 0.4510 · 0.7260 |
(11,14,19) |
| 1 | 0.2768 · 0.4571 · 0.7320 |
(5,13,16) |
| 1 | 0.2534 · 0.4840 · 0.7354 |
(1,17,21) |
| 1 | 0.2611 · 0.4797 · 0.7388 |
(6,12,23) |
| 1 | 0.2765 · 0.4763 · 0.7510 |
(3,8,20) |
| 1 | 0.3037 · 0.4697 · 0.7718 |
(0,2,21) |
| 1 | 0.3011 · 0.4754 · 0.7749 |
(7,15,23) |
| 1 | 0.3298 · 0.4500 · 0.7783 |
(7,8,12) |
| 1 | 0.2312 · 0.5923 · 0.8219 |
(2,6,24) |
| 1 | 0.2769 · 0.5823 · 0.8579 |
(0,11,14) |
| 1 | 0.2173 · 0.6631 · 0.8790 |
(1,2,7) |
| 1 | 0.2225 · 0.6584 · 0.8796 |
(4,14,20) |
| 1 | 0.2258 · 0.6559 · 0.8803 |
(9,13,18) |
| 1 | 0.2765 · 0.6092 · 0.8845 |
(3,8,22) |
| 1 | 0.3037 · 0.5823 · 0.8848 |
(0,14,21) |
| 1 | 0.2301 · 0.6575 · 0.8863 |
(0,12,15) |
| 1 | 0.3011 · 0.5875 · 0.8875 |
(7,13,23) |
| 1 | 0.2813 · 0.6092 · 0.8894 |
(3,10,22) |
| 1 | 0.2258 · 0.6674 · 0.8919 |
(3,17,19) |
| 1 | 0.2359 · 0.6671 · 0.9018 |
(6,16,22) |
| 1 | 0.1670 · 0.7573 · 0.9228 |
(2,9,14) |
| 1 | 0.1675 · 0.7580 · 0.9241 |
(4,13,15) |
| 1 | 0.3016 · 0.6924 · 0.9932 |
(4,7,24) |
| 1 | 0.4452 · 0.5905 · 1.0351 |
(1,15,24) |
| 1 | 0.4453 · 0.6410 · 1.0858 |
(3,11,15) |
| 1 | 0.4470 · 0.6412 · 1.0876 |
(2,5,22) |
| 1 | 0.4800 · 0.6085 · 1.0880 |
(8,14,16) |
| 1 | 0.4891 · 0.6045 · 1.0930 |
(10,13,19) |
| 1 | 0.4830 · 0.6212 · 1.1037 |
(0,18,23) |
| 1 | 0.2312 · 0.9051 · 1.1355 |
(6,17,24) |
| 1 | 0.2768 · 0.9153 · 1.1916 |
(5,8,13) |
| 1 | 0.3037 · 0.8976 · 1.2008 |
(0,5,21) |
| 1 | 0.3228 · 0.8845 · 1.2068 |
(8,21,22) |
| 1 | 0.3285 · 0.8894 · 1.2175 |
(3,10,23) |
| 1 | 0.4532 · 0.9114 · 1.3642 |
(10,20,24) |
| 1 | 0.4355 · 0.9472 · 1.3824 |
(16,21,24) |
Provenance
- Found by Rhys Chappell, August 2026.
- Coordinates by an external contributor, re-verified here:
github.com/rhyschappell (surgery/cascade search)— Improves the previous value 0.008877423784 by 4.94%. Found by point insertion/deletion surgery between neighboring record configurations followed by constrained local maximin refinement.. - Verified in exact arithmetic: all 2300 triples enumerated, 45 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
