Convex, n = 35 record
A = 0.004773805331154…
full precision
Exact value of the published coordinate literals:
0.00477380533115438047457428332165
Symmetry
Symmetry
5-fold dihedral symmetry (group D5, order 10).
35 points in 4 orbits (10 + 10 + 10 + 5) — hover a point to see its orbit.
Minimal triangles
70 triangles tied (within relative 10−9) at the minimal area, in 7 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 10 | 0.1670 · 0.3412 · 0.5056 |
(0,1,34) (0,4,33) (1,2,30) (2,3,31) (3,4,32) (5,6,32) (5,9,31) (6,7,33) (7,8,34) (8,9,30) |
| 10 | 0.1606 · 0.3497 · 0.5078 |
(10,17,20) (10,17,27) (11,18,21) (11,18,28) (12,19,22) (12,19,29) (13,15,23) (13,15,25) (14,16,24) (14,16,26) |
| 10 | 0.1606 · 0.6924 · 0.8523 |
(10,11,20) (10,14,24) (11,12,21) (12,13,22) (13,14,23) (15,16,26) (15,19,25) (16,17,27) (17,18,28) (18,19,29) |
| 10 | 0.2851 · 0.6697 · 0.9543 |
(0,8,20) (0,8,28) (1,9,21) (1,9,29) (2,5,22) (2,5,25) (3,6,23) (3,6,26) (4,7,24) (4,7,27) |
| 10 | 0.3762 · 0.5838 · 0.9596 |
(0,16,21) (1,17,22) (2,18,23) (3,19,24) (4,15,20) (5,14,29) (6,10,25) (7,11,26) (8,12,27) (9,13,28) |
| 10 | 0.1600 · 0.8591 · 1.0186 |
(0,9,10) (0,9,19) (1,5,11) (1,5,15) (2,6,12) (2,6,16) (3,7,13) (3,7,17) (4,8,14) (4,8,18) |
| 10 | 0.4723 · 0.6212 · 1.0933 |
(10,28,34) (11,29,30) (12,25,31) (13,26,32) (14,27,33) (15,22,31) (16,23,32) (17,24,33) (18,20,34) (19,21,30) |
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— 5-fold dihedral symmetric; 70 tied minimal triangles. - Verified in exact arithmetic: all 6545 triples enumerated, 70 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
