Convex, n = 36 record
A = 0.004816521217255…
full precision
Exact value of the published coordinate literals:
0.00481652121725546850971056770181
Classes
Symmetry
Symmetry
9-fold dihedral symmetry (group D9, order 18).
36 points in 3 orbits (18 + 9 + 9) — hover a point to see its orbit.
Minimal triangles
72 triangles tied (within relative 10−9) at the minimal area, in 4 congruence classes:
| count | side lengths | triangles (point indices) | |
|---|---|---|---|
| 18 | 0.1399 · 0.5943 · 0.7335 |
(0,2,30) (0,7,28) (1,3,31) (1,8,29) (2,4,32) (3,5,33) (4,6,34) (5,7,35) (6,8,27) (9,11,33) (9,16,35) (10,12,32) … | |
| 18 | 0.1399 · 0.6185 · 0.7576 |
(0,30,32) (1,31,33) (2,32,34) (3,33,35) (4,27,34) (5,28,35) (6,27,29) (7,28,30) (8,29,31) (9,31,33) (10,30,32) (11,29,31) … | |
| 18 | 0.2634 · 0.5581 · 0.8212 |
(0,21,24) (1,22,25) (2,23,26) (3,18,24) (4,19,25) (5,20,26) (6,18,21) (7,19,22) (8,20,23) (9,21,24) (10,20,23) (11,19,22) … | |
| 18 | 0.3127 · 0.5412 · 0.8536 |
(0,19,27) (1,20,28) (2,21,29) (3,22,30) (4,23,31) (5,24,32) (6,25,33) (7,26,34) (8,18,35) (9,26,27) (10,25,35) (11,24,34) … |
Provenance
- Found by Nathan Sudermann-Merx, October 2026.
- Coordinates by an external contributor, re-verified here:
Nathan Sudermann-Merx search campaign, October 2026: C basin hopping with soft-min L-BFGS, symmetric orbit parametrisation, ruin-and-recreate moves, vertical seeding from n-1/n+1 records, HiGHS trust-region SLP polish— Found by vertical seeding / basin hopping; coordinates are the SLP-polished double-precision optimum, truncated toward zero.. - Verified in exact arithmetic: all 7140 triples enumerated, 72 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
