Convex, n = 30 record reconstructed coords

A = 0.005942472777212…

full precision

Exact value of the published coordinate literals: 0.00594247277721246942266161515028

54 triangles tie for the minimal area.

Symmetry

Approximately 180° Rotationally symmetric (group C2: the configuration sits within ~10⁻⁴ of exact symmetry, but the optimum is not exactly symmetric at coordinate precision). (Friedman's page says: 6-fold dihedral symmetry.)

Minimal triangles

54 triangles tied (within relative 10⁻⁹) at the minimal area, in 27 congruence classes:

count	side lengths	triangles (point indices)
2	`37.4468 · 83.6991 · 120.9099`	(0,3,26) (1,2,15)
2	`37.4623 · 83.6991 · 120.9255`	(0,3,8) (1,2,11)
2	`37.4589 · 83.7323 · 120.9554`	(0,21,22) (1,19,20)
2	`37.4789 · 83.7323 · 120.9756`	(0,21,23) (1,18,20)
2	`37.5148 · 83.8441 · 121.1242`	(2,4,20) (3,7,21)
2	`37.5194 · 83.8441 · 121.1288`	(2,14,20) (3,21,27)
2	`28.4695 · 110.6238 · 138.8888`	(2,17,19) (3,22,24)
2	`28.4726 · 110.6484 · 138.9165`	(13,15,20) (21,26,28)
2	`28.5013 · 110.7119 · 139.0093`	(0,5,7) (1,4,12)
2	`28.5139 · 110.7626 · 139.0728`	(0,10,27) (1,9,14)
2	`28.5147 · 110.8191 · 139.1303`	(6,8,21) (11,20,29)
2	`28.5242 · 110.8452 · 139.1660`	(2,16,18) (3,23,25)
2	`64.9905 · 101.7895 · 166.6991`	(6,20,22) (19,21,29)
2	`65.0073 · 101.7959 · 166.7224`	(4,13,21) (7,20,28)
2	`65.0134 · 101.8290 · 166.7616`	(2,25,26) (3,15,16)
2	`65.0352 · 101.8373 · 166.7917`	(2,24,27) (3,14,17)
2	`65.1074 · 101.9680 · 166.9950`	(0,9,11) (1,8,10)
2	`65.1124 · 101.9699 · 167.0018`	(0,12,18) (1,5,23)
2	`81.2236 · 92.4388 · 173.5939`	(8,20,24) (11,17,21)
2	`81.2438 · 92.4656 · 173.6410`	(2,23,28) (3,13,18)
2	`81.2810 · 92.4895 · 173.7021`	(5,20,26) (12,15,21)
2	`81.3182 · 92.5313 · 173.7812`	(2,10,22) (3,9,19)
2	`81.3690 · 92.6064 · 173.9073`	(0,14,29) (1,6,27)
2	`81.3860 · 92.6214 · 173.9393`	(0,4,16) (1,7,25)
2	`101.7895 · 101.7959 · 203.5432`	(6,20,28) (13,21,29)
2	`101.8290 · 101.8373 · 203.6240`	(2,24,25) (3,16,17)
2	`101.9680 · 101.9699 · 203.8959`	(0,9,12) (1,5,10)

Provenance

Found by Nathan Sudermann-Merx, August 2026.
Coordinates reconstructed by local optimization: heilbronn-site reconstruct/reconstruct.py — re-polished from the published record figure — the record holder's arrangement with re-derived coordinates.
Verified in exact arithmetic: all 4060 triples enumerated, 54 tied at the minimum.
Friedman's page lists: A = .005942+.

Downloads

points.txt coordinates, tab-separated
points.csv coordinates, CSV
points.json full record: value, provenance, verification
figure.svg this figure