Convex, n = 28 record reconstructed coords
A = 0.007627719003112…
full precision
Exact value of the published coordinate literals:
0.00762771900311235552753085690762
Symmetry
Not symmetric (group C1, order 1). (Friedman's page says: 7-fold dihedral symmetry.)
Minimal triangles
49 triangles tied (within relative 10−9) at the minimal area, in 33 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 2 | 33.0050 · 60.3812 · 92.4858 |
(0,6,16) (6,16,27) |
| 2 | 33.0101 · 60.3778 · 92.4877 |
(3,19,22) (3,20,24) |
| 2 | 33.0319 · 60.4161 · 92.5495 |
(1,9,20) (2,9,22) |
| 2 | 33.0319 · 60.4278 · 92.5615 |
(1,14,20) (2,17,22) |
| 2 | 64.8818 · 109.8059 · 174.5563 |
(7,13,14) (8,12,17) |
| 2 | 64.8829 · 109.8140 · 174.5655 |
(9,11,21) (9,18,26) |
| 2 | 64.9241 · 109.8733 · 174.6661 |
(0,5,11) (4,18,27) |
| 2 | 64.9253 · 109.8871 · 174.6813 |
(8,24,25) (13,19,23) |
| 2 | 64.9350 · 109.8971 · 174.7010 |
(0,7,26) (12,21,27) |
| 2 | 83.0196 · 92.4877 · 175.3859 |
(10,19,22) (15,20,24) |
| 2 | 83.0226 · 92.4858 · 175.3870 |
(0,13,16) (6,8,27) |
| 2 | 83.0774 · 92.5451 · 175.5014 |
(4,6,24) (5,16,19) |
| 2 | 83.0732 · 92.5495 · 175.5016 |
(1,9,12) (2,7,9) |
| 2 | 83.0880 · 92.5615 · 175.5285 |
(14,20,23) (17,22,25) |
| 2 | 103.9670 · 103.9707 · 207.8650 |
(6,10,12) (7,15,16) |
| 2 | 104.0342 · 104.0363 · 207.9979 |
(1,4,21) (2,5,26) |
| 1 | 33.0101 · 60.3995 · 92.5100 |
(0,3,22) |
| 1 | 33.0106 · 60.4005 · 92.5114 |
(3,20,27) |
| 1 | 33.0220 · 60.3930 · 92.5155 |
(1,16,17) |
| 1 | 33.0225 · 60.3939 · 92.5170 |
(2,6,14) |
| 1 | 33.0220 · 60.4206 · 92.5438 |
(1,16,19) |
| 1 | 33.0225 · 60.4213 · 92.5451 |
(2,6,24) |
| 1 | 64.8995 · 109.8311 · 174.5993 |
(10,23,24) |
| 1 | 64.9005 · 109.8327 · 174.6019 |
(15,19,25) |
| 1 | 64.9021 · 109.8499 · 174.6208 |
(5,14,15) |
| 1 | 64.9032 · 109.8517 · 174.6236 |
(4,10,17) |
| 1 | 83.0469 · 92.5100 · 175.4356 |
(0,3,21) |
| 1 | 83.0417 · 92.5155 · 175.4359 |
(1,17,18) |
| 1 | 83.0483 · 92.5114 · 175.4384 |
(3,26,27) |
| 1 | 83.0430 · 92.5170 · 175.4387 |
(2,11,14) |
| 1 | 103.9515 · 103.9516 · 207.8303 |
(3,11,18) |
| 1 | 104.0025 · 104.0071 · 207.9369 |
(8,22,23) |
| 1 | 104.0041 · 104.0087 · 207.9402 |
(13,20,25) |
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 3276 triples enumerated, 49 tied at the minimum.
- Friedman's page lists:
A = .007627+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
