{
 "schema_version": 1,
 "variant": "convex",
 "n": 18,
 "frame": "free",
 "points": [
  [
   "0.579401501191424",
   "0.084102051429217"
  ],
  [
   "0.579401501191424",
   "-0.084102051429216"
  ],
  [
   "0.259455946521507",
   "0"
  ],
  [
   "0.216866237547625",
   "0.543827444737221"
  ],
  [
   "0.362535263643799",
   "0.459725393308005"
  ],
  [
   "0.129727973260754",
   "0.224695440850562"
  ],
  [
   "-0.362535263643799",
   "0.459725393308005"
  ],
  [
   "-0.216866237547625",
   "0.543827444737221"
  ],
  [
   "-0.129727973260754",
   "0.224695440850562"
  ],
  [
   "-0.579401501191424",
   "-0.084102051429216"
  ],
  [
   "-0.579401501191424",
   "0.084102051429217"
  ],
  [
   "-0.259455946521507",
   "0"
  ],
  [
   "-0.216866237547625",
   "-0.543827444737221"
  ],
  [
   "-0.362535263643799",
   "-0.459725393308005"
  ],
  [
   "-0.129727973260754",
   "-0.224695440850562"
  ],
  [
   "0.362535263643799",
   "-0.459725393308005"
  ],
  [
   "0.216866237547625",
   "-0.543827444737221"
  ],
  [
   "0.129727973260754",
   "-0.224695440850562"
  ]
 ],
 "value": {
  "decimal": "0.0182388954634908723600644432595",
  "fraction": "5211112989568819048894923327/285714285714285625167971022578",
  "published": "A = [2 - (3/2 - √(239/3)/6)^(1/3) - (3/2 + √(239/3)/6)^(1/3)] / 18",
  "published_decimal": "0.018238",
  "published_lower_bound": true,
  "exact_text": "[2 - (3/2 - √(239/3)/6)^(1/3) - (3/2 + √(239/3)/6)^(1/3)] / 18",
  "exact_sympy": "(2 - cbrt(Rational(3,2) - sqrt(Rational(239,3))/6) - cbrt(Rational(3,2) + sqrt(Rational(239,3))/6))/18",
  "minimal_polynomial": "1944*v**3 - 648*v**2 + 66*v - 1",
  "exact_display": "[2 − ∛(3/2 − √(239/3)/6) − ∛(3/2 + √(239/3)/6)] / 18",
  "exact_poly": {
   "poly": "1944*v**3 - 648*v**2 + 66*v - 1",
   "near": 0.0182,
   "which": "smallest real"
  },
  "exact_decimal": "0.0182388954634910572362139010433579317373186207",
  "exact_mathml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mfrac><mrow><mrow><mn>2</mn><mo>−</mo><mroot><mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><msqrt><mfrac><mrow><mn>239</mn></mrow><mrow><mn>3</mn></mrow></mfrac></msqrt></mrow><mrow><mn>6</mn></mrow></mfrac></mrow></mrow><mn>3</mn></mroot><mo>−</mo><mroot><mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mfrac><mrow><mn>239</mn></mrow><mrow><mn>3</mn></mrow></mfrac></msqrt></mrow><mrow><mn>6</mn></mrow></mfrac></mrow></mrow><mn>3</mn></mroot></mrow></mrow><mrow><mn>18</mn></mrow></mfrac></math>",
  "poly_mathml": "<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>1944</mn><msup><mi>v</mi><mn>3</mn></msup><mo>−</mo><mn>648</mn><msup><mi>v</mi><mn>2</mn></msup><mo>+</mo><mn>66</mn><mi>v</mi><mo>−</mo><mn>1</mn></mrow></math>"
 },
 "status": "record",
 "page_relation": "OK",
 "credit": {
  "found": {
   "name": "Tej Stead",
   "date": "July 2026"
  },
  "proved": null,
  "trivial": false
 },
 "coordinates_source": {
  "kind": "author",
  "ref": "TejSteadQC/heilbronn-configurations claims/03-exact-convex-n18",
  "note": null
 },
 "coordinates_reconstructed": false,
 "symmetry": {
  "label": "6-fold dihedral symmetry"
 },
 "notes": [],
 "changelog": [],
 "references": [],
 "verify": {
  "n": 18,
  "triples_checked": 816,
  "value": "0.0182388954634908723600644432595",
  "value_fraction": "5211112989568819048894923327/285714285714285625167971022578",
  "min_triple": [
   0,
   12,
   17
  ],
  "num_min_ties": 36,
  "feasible": true,
  "violations": [],
  "hull_vertex_count": 12
 }
}