{
 "schema_version": 1,
 "variant": "triangle",
 "n": 8,
 "frame": "right",
 "points": [
  [
   "0.888607734966284",
   "0.111392265033716"
  ],
  [
   "0.11199970565403",
   "0"
  ],
  [
   "0.720562726018855",
   "0"
  ],
  [
   "0.43930709783921",
   "0.484405907813651"
  ],
  [
   "0.395276367904075",
   "0.212129872844957"
  ],
  [
   "0",
   "0.155433665397645"
  ],
  [
   "0.11199970565403",
   "0.605262423310289"
  ],
  [
   "0",
   "1"
  ]
 ],
 "value": {
  "decimal": "0.067789213254196898218756861476",
  "fraction": "16947303313549224554689215369/250000000000000000000000000000",
  "published": "A = .0677+",
  "published_decimal": "0.0677",
  "published_lower_bound": true,
  "exact_text": null,
  "exact_sympy": null,
  "minimal_polynomial": "1216512*t**7 + 1022976*t**6 - 2745456*t**5 + 2218730*t**4 + 32206304*t**3 - 19148615*t**2 + 3156103*t - 86233",
  "exact_poly": {
   "poly": "1216512*t**7 + 1022976*t**6 - 2745456*t**5 + 2218730*t**4 + 32206304*t**3 - 19148615*t**2 + 3156103*t - 86233",
   "near": 0.0339,
   "which": "root near 0.0339",
   "scale": 2,
   "note": "polynomial for the unit right triangle; A is twice its root"
  },
  "exact_decimal": "0.0677892132541972123588108049740286304958007014",
  "poly_mathml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>1216512</mn><msup><mi>t</mi><mn>7</mn></msup><mo>+</mo><mn>1022976</mn><msup><mi>t</mi><mn>6</mn></msup><mo>−</mo><mn>2745456</mn><msup><mi>t</mi><mn>5</mn></msup><mo>+</mo><mn>2218730</mn><msup><mi>t</mi><mn>4</mn></msup><mo>+</mo><mn>32206304</mn><msup><mi>t</mi><mn>3</mn></msup><mo>−</mo><mn>19148615</mn><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mn>3156103</mn><mi>t</mi><mo>−</mo><mn>86233</mn></mrow></math>"
 },
 "status": "proven",
 "page_relation": "OK",
 "credit": {
  "found": {
   "name": "David Cantrell",
   "date": "July 2006"
  },
  "proved": {
   "name": "Nathan Sudermann-Merx",
   "date": "2026"
  },
  "trivial": false
 },
 "coordinates_source": {
  "kind": "reconstructed",
  "ref": "heilbronn-site reconstruct/reconstruct.py",
  "note": "reconstructed by local optimization; matches published value 0.0677+ and symmetry (Not symmetric)"
 },
 "coordinates_reconstructed": true,
 "symmetry": {
  "label": "Not symmetric"
 },
 "notes": [],
 "changelog": [],
 "references": [
  "sudermann-merx-2026-triangle",
  "chen-zeng-zhou-2014"
 ],
 "verify": {
  "n": 8,
  "triples_checked": 56,
  "value": "0.067789213254196898218756861476",
  "value_fraction": "16947303313549224554689215369/250000000000000000000000000000",
  "min_triple": [
   0,
   3,
   7
  ],
  "num_min_ties": 11,
  "feasible": true,
  "violations": [],
  "hull_vertex_count": null
 }
}