Triangle, n = 23 record

A = 0.009269781872931…
full precision

Exact value of the published coordinate literals: 0.00926978187293123013824208706900

42 triangles tie for the minimal area.

Symmetry

Mirror symmetric (group D1, order 2).

23 points in 12 orbits (2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 1) — hover a point to see its orbit.

Minimal triangles

42 triangles tied (within relative 10−9) at the minimal area, in 21 congruence classes:

countside lengthstriangles (point indices)
2 0.2128 · 0.2201 · 0.4240 (5,7,11) (7,11,14)
2 0.3086 · 0.3579 · 0.6641 (2,8,12) (3,6,22)
2 0.3257 · 0.3531 · 0.6766 (4,5,20) (9,10,14)
2 0.2546 · 0.4363 · 0.6886 (0,2,6) (2,6,21)
2 0.2523 · 0.4517 · 0.7019 (1,5,17) (13,14,19)
2 0.2764 · 0.4501 · 0.7247 (0,8,20) (3,9,21)
2 0.3129 · 0.4236 · 0.7347 (2,9,19) (6,17,20)
2 0.2925 · 0.4473 · 0.7380 (7,17,22) (11,12,19)
2 0.2523 · 0.4953 · 0.7458 (1,5,15) (13,14,15)
2 0.3091 · 0.4605 · 0.7681 (0,4,7) (10,11,21)
2 0.2201 · 0.6156 · 0.8342 (5,7,12) (11,14,22)
2 0.2764 · 0.5659 · 0.8410 (0,9,20) (9,20,21)
2 0.2129 · 0.6397 · 0.8511 (1,4,9) (10,13,20)
2 0.2925 · 0.5672 · 0.8585 (12,16,19) (17,18,22)
2 0.2262 · 0.6423 · 0.8671 (2,3,18) (6,8,16)
2 0.1621 · 0.7149 · 0.8753 (1,10,12) (4,13,22)
2 0.3316 · 0.5672 · 0.8977 (12,15,16) (15,18,22)
2 0.1778 · 0.7220 · 0.8983 (3,14,20) (5,8,9)
2 0.4508 · 0.5910 · 1.0411 (3,12,17) (8,19,22)
2 0.4605 · 0.5948 · 1.0548 (0,4,16) (10,18,21)
2 0.3326 · 0.8977 · 1.2299 (0,15,22) (12,15,21)

Provenance

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