Square, n = 15 record
A = 0.021210541005490…
full precision
Exact value of the published coordinate literals:
0.0212105410054906282998648191905
Symmetry
Not symmetric (group C1, order 1).
Minimal triangles
25 triangles tied (within relative 10−9) at the minimal area, in 25 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 1 | 0.3181 · 0.3185 · 0.6218 |
(1,7,9) |
| 1 | 0.3169 · 0.3265 · 0.6291 |
(0,2,14) |
| 1 | 0.3027 · 0.3463 · 0.6350 |
(6,10,11) |
| 1 | 0.2836 · 0.4010 · 0.6724 |
(1,2,12) |
| 1 | 0.2827 · 0.4104 · 0.6814 |
(4,6,13) |
| 1 | 0.2865 · 0.4072 · 0.6821 |
(7,11,14) |
| 1 | 0.3185 · 0.4163 · 0.7252 |
(1,9,14) |
| 1 | 0.3851 · 0.4967 · 0.8763 |
(5,7,10) |
| 1 | 0.3214 · 0.6063 · 0.9226 |
(5,6,8) |
| 1 | 0.3227 · 0.6103 · 0.9281 |
(4,10,12) |
| 1 | 0.2865 · 0.6541 · 0.9355 |
(7,8,14) |
| 1 | 0.3209 · 0.6218 · 0.9378 |
(1,7,13) |
| 1 | 0.3189 · 0.6291 · 0.9432 |
(2,3,14) |
| 1 | 0.2853 · 0.6724 · 0.9528 |
(2,5,12) |
| 1 | 0.2835 · 0.6762 · 0.9547 |
(0,8,9) |
| 1 | 0.2864 · 0.6814 · 0.9629 |
(3,6,13) |
| 1 | 0.3214 · 0.7053 · 1.0228 |
(4,5,8) |
| 1 | 0.3189 · 0.7252 · 1.0403 |
(1,3,14) |
| 1 | 0.2853 · 0.7796 · 1.0611 |
(0,5,12) |
| 1 | 0.4967 · 0.6527 · 1.1470 |
(5,10,13) |
| 1 | 0.4437 · 0.7087 · 1.1499 |
(0,6,7) |
| 1 | 0.3463 · 0.8114 · 1.1549 |
(1,6,11) |
| 1 | 0.3456 · 0.8176 · 1.1604 |
(2,4,9) |
| 1 | 0.3463 · 0.9527 · 1.2969 |
(2,6,11) |
| 1 | 0.5011 · 0.8763 · 1.3760 |
(3,5,7) |
Provenance
- Found by Nathan Sudermann-Merx, August 2026.
- Coordinates by an external contributor, re-verified here:
Original full-precision coordinates of Nathan Sudermann-Merx's August 2026 record submissions— Fully asymmetric and rigid; replaced Karpov's 2011 entry. orbit-seeded searcher (LP relocation, min-norm ascent), finished by sign-fixed cell QCP and equal-critical-area continuation. - Verified in exact arithmetic: all 455 triples enumerated, 25 tied at the minimum.
Record history
- 2011-08 0.0211056819 — Peter Karpov (coordinates published 2018 at inversed.ru/Ascension)
- 2026-08 0.0211061686 — in-basin tightening of Karpov's coordinates (this site)
- 2026-08-21 .02121+ — Nathan Sudermann-Merx (coordinates never published)
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
