Convex, n = 27 record
A = 0.007803760273721…
full precision
Exact value of the published coordinate literals:
0.00780376027372161968567885631627
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: no symmetry.)
Minimal triangles
45 triangles tied (within relative 10−9) at the minimal area, in 45 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.1680 · 0.3192 · 0.4823 |
(13,16,22) |
| 1 | 0.1756 · 0.3139 · 0.4848 |
(5,6,10) |
| 1 | 0.1766 · 0.3136 · 0.4855 |
(12,16,19) |
| 1 | 0.1704 · 0.3200 · 0.4857 |
(14,19,20) |
| 1 | 0.1756 · 0.3165 · 0.4876 |
(6,10,18) |
| 1 | 0.1680 · 0.3250 · 0.4883 |
(5,13,16) |
| 1 | 0.1766 · 0.3167 · 0.4888 |
(16,18,19) |
| 1 | 0.1801 · 0.3134 · 0.4890 |
(9,13,20) |
| 1 | 0.1754 · 0.3191 · 0.4899 |
(10,14,22) |
| 1 | 0.1685 · 0.3264 · 0.4903 |
(6,9,12) |
| 1 | 0.1685 · 0.3268 · 0.4907 |
(6,7,9) |
| 1 | 0.1704 · 0.3304 · 0.4964 |
(7,14,19) |
| 1 | 0.1754 · 0.3266 · 0.4976 |
(3,10,14) |
| 1 | 0.1801 · 0.3255 · 0.5015 |
(3,9,13) |
| 1 | 0.1814 · 0.3339 · 0.5113 |
(17,21,25) |
| 1 | 0.2243 · 0.3527 · 0.5742 |
(18,22,26) |
| 1 | 0.2362 · 0.6433 · 0.8786 |
(3,12,17) |
| 1 | 0.3189 · 0.5724 · 0.8906 |
(8,20,26) |
| 1 | 0.4153 · 0.4883 · 0.9030 |
(5,16,26) |
| 1 | 0.2243 · 0.6810 · 0.9044 |
(11,22,26) |
| 1 | 0.4228 · 0.4855 · 0.9077 |
(12,19,23) |
| 1 | 0.3460 · 0.5635 · 0.9088 |
(17,20,24) |
| 1 | 0.4257 · 0.4876 · 0.9126 |
(1,6,18) |
| 1 | 0.4302 · 0.4857 · 0.9152 |
(11,14,20) |
| 1 | 0.4261 · 0.4899 · 0.9154 |
(2,10,22) |
| 1 | 0.4280 · 0.4890 · 0.9164 |
(0,9,20) |
| 1 | 0.4334 · 0.4848 · 0.9176 |
(5,10,15) |
| 1 | 0.4224 · 0.4976 · 0.9194 |
(3,14,24) |
| 1 | 0.4186 · 0.5015 · 0.9194 |
(3,13,21) |
| 1 | 0.4416 · 0.4888 · 0.9297 |
(16,17,18) |
| 1 | 0.3613 · 0.5703 · 0.9310 |
(4,12,25) |
| 1 | 0.4411 · 0.4907 · 0.9312 |
(7,8,9) |
| 1 | 0.4386 · 0.4964 · 0.9343 |
(7,19,25) |
| 1 | 0.4562 · 0.4823 · 0.9379 |
(4,13,22) |
| 1 | 0.2001 · 0.7780 · 0.9774 |
(2,16,20) |
| 1 | 0.2037 · 0.7758 · 0.9786 |
(0,19,22) |
| 1 | 0.2012 · 0.7829 · 0.9833 |
(8,14,18) |
| 1 | 0.2112 · 0.7874 · 0.9979 |
(3,6,25) |
| 1 | 0.5321 · 0.5357 · 1.0674 |
(0,10,23) |
| 1 | 0.5295 · 0.5413 · 1.0704 |
(15,19,21) |
| 1 | 0.5319 · 0.5420 · 1.0735 |
(8,16,24) |
| 1 | 0.5414 · 0.5449 · 1.0859 |
(1,13,25) |
| 1 | 0.5354 · 0.5578 · 1.0928 |
(2,9,17) |
| 1 | 0.5423 · 0.5567 · 1.0986 |
(4,6,11) |
| 1 | 0.4153 · 0.7016 · 1.1166 |
(1,16,26) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates from this site's companion repository:
TejSteadQC/heilbronn-configurations claims-2026-08-20/convex-n27. - Verified in exact arithmetic: all 2925 triples enumerated, 45 tied at the minimum.
- Friedman's page lists:
A = .007798+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
