Square, n = 16 record
A =
= 0.0205278592375366568914956011730205278592375367…
Symmetry
Symmetry
180° Rotationally symmetric (group C2, order 2).
Minimal triangles
64 triangles tied (within relative 10−9) at the minimal area, in 15 congruence classes:
| count | side lengths | triangles (point indices) |
|---|---|---|
| 8 | 0.3098 · 0.3395 · 0.6364 |
(0,4,15) (1,5,14) (2,9,12) (3,8,13) (4,7,15) (5,6,14) (8,10,13) (9,11,12) |
| 8 | 0.2651 · 0.4237 · 0.6774 |
(0,2,10) (1,3,11) (2,6,10) (3,7,11) (4,8,12) (5,9,13) (8,12,14) (9,13,15) |
| 8 | 0.2651 · 0.6774 · 0.9374 |
(0,2,6) (0,6,10) (1,3,7) (1,7,11) (4,8,14) (4,12,14) (5,9,15) (5,13,15) |
| 8 | 0.3098 · 0.6364 · 0.9416 |
(0,4,7) (0,7,15) (1,5,6) (1,6,14) (2,9,11) (2,11,12) (3,8,10) (3,10,13) |
| 4 | 0.3098 · 0.3344 · 0.6309 |
(6,9,14) (7,8,15) (8,10,15) (9,11,14) |
| 4 | 0.2651 · 0.4297 · 0.6837 |
(0,10,12) (1,11,13) (10,12,14) (11,13,15) |
| 4 | 0.3395 · 0.4119 · 0.7432 |
(0,8,13) (1,9,12) (2,5,14) (3,4,15) |
| 4 | 0.3098 · 0.6309 · 0.9361 |
(6,9,11) (6,11,14) (7,8,10) (7,10,15) |
| 4 | 0.2651 · 0.6837 · 0.9438 |
(0,10,14) (0,12,14) (1,11,15) (1,13,15) |
| 2 | 0.2651 · 0.5554 · 0.8134 |
(4,8,9) (5,8,9) |
| 2 | 0.4035 · 0.5302 · 0.9294 |
(6,12,13) (7,12,13) |
| 2 | 0.2651 · 0.8134 · 1.0748 |
(4,5,8) (4,5,9) |
| 2 | 0.4035 · 0.6977 · 1.0985 |
(6,12,15) (7,13,14) |
| 2 | 0.4119 · 0.7123 · 1.1217 |
(0,8,11) (1,9,10) |
| 2 | 0.4035 · 0.9294 · 1.3313 |
(6,7,12) (6,7,13) |
Provenance
- Found by Mark Beyleveld, August 2006.
- Coordinates from spiralulam/heilbronn (MIT):
spiralulam/heilbronn config_n16.json— Beyleveld (unpublished). - Verified in exact arithmetic: all 560 triples enumerated, 64 tied at the minimum.
- Friedman's page lists:
A = 7 / 341 = .02053+.
Downloads
- points.txt coordinates, tab-separated
- points.csv coordinates, CSV
- points.json full record: value, provenance, verification
- figure.svg this figure
