[
  {
    "system": "tet_oct",
    "component": "Tetrahedron",
    "edgeCount": 6,
    "dihedralCosines": [
      {
        "sign": 1,
        "square": "1/9"
      }
    ],
    "heesch": 0,
    "verified": true,
    "certificate": "uniform-edge-angle",
    "maximumEdgeSectors": 5,
    "checks": [
      {
        "edgeSectors": 1,
        "cosineSquaredOfAngleSum": "1/9"
      },
      {
        "edgeSectors": 2,
        "cosineSquaredOfAngleSum": "49/81"
      },
      {
        "edgeSectors": 3,
        "cosineSquaredOfAngleSum": "529/729"
      },
      {
        "edgeSectors": 4,
        "cosineSquaredOfAngleSum": "289/6561"
      },
      {
        "edgeSectors": 5,
        "cosineSquaredOfAngleSum": "58081/59049"
      }
    ],
    "scope": "All Euclidean rigid motions; generic root-edge point permits edge sectors and flat-face half-spaces. No face-to-face assumption."
  },
  {
    "system": "tet_oct",
    "component": "Octahedron",
    "edgeCount": 12,
    "dihedralCosines": [
      {
        "sign": -1,
        "square": "1/9"
      }
    ],
    "heesch": 0,
    "verified": true,
    "certificate": "uniform-edge-angle",
    "maximumEdgeSectors": 3,
    "checks": [
      {
        "edgeSectors": 1,
        "cosineSquaredOfAngleSum": "1/9"
      },
      {
        "edgeSectors": 2,
        "cosineSquaredOfAngleSum": "49/81"
      },
      {
        "edgeSectors": 3,
        "cosineSquaredOfAngleSum": "529/729"
      }
    ],
    "scope": "All Euclidean rigid motions; generic root-edge point permits edge sectors and flat-face half-spaces. No face-to-face assumption."
  },
  {
    "system": "perovskite",
    "component": "Cuboctahedron",
    "edgeCount": 24,
    "dihedralCosines": [
      {
        "sign": -1,
        "square": "1/3"
      }
    ],
    "heesch": 0,
    "verified": true,
    "certificate": "uniform-edge-angle",
    "maximumEdgeSectors": 3,
    "checks": [
      {
        "edgeSectors": 1,
        "cosineSquaredOfAngleSum": "1/3"
      },
      {
        "edgeSectors": 2,
        "cosineSquaredOfAngleSum": "1/9"
      },
      {
        "edgeSectors": 3,
        "cosineSquaredOfAngleSum": "25/27"
      }
    ],
    "scope": "All Euclidean rigid motions; generic root-edge point permits edge sectors and flat-face half-spaces. No face-to-face assumption."
  },
  {
    "system": "laves_c15",
    "component": "TruncTetra",
    "edgeCount": 18,
    "dihedralCosines": [
      {
        "sign": -1,
        "square": "1/9"
      },
      {
        "sign": 1,
        "square": "1/9"
      }
    ],
    "heesch": null,
    "verified": false,
    "status": "This angle test does not decide the mixed-dihedral case."
  }
]