static const double vertices[][3][3] = {
  { { 0, 0, 0}, {1+sqrt(8), 1+sqrt(2), 1}, {1+sqrt(2), 1+sqrt(2), 1} },
  { { 0, 0, 0}, {1+sqrt(8), 1+sqrt(2), 1}, {sqrt(8), sqrt(2), 0} },
  { { 0, 0, 0}, {1+sqrt(8), 1+sqrt(2), 1}, {1+sqrt(2), 1, 1} },
  { { 2, 0, 0}, {-(1+sqrt(8)), 1+sqrt(2), 1}, {-(1+sqrt(2)), 1+sqrt(2), 1} },
  { { 2, 0, 0}, {-(1+sqrt(8)), 1+sqrt(2), 1}, {-sqrt(8), sqrt(2), 0} },
  { { 2, 0, 0}, {-(1+sqrt(8)), 1+sqrt(2), 1}, {-(1+sqrt(2)), 1, 1} },
  { { 1, 1, 1}, {0, -sqrt(2), -sqrt(8)}, {-sqrt(0.5), -sqrt(0.5), -sqrt(4.5)} },
  { { 1, 1, 1}, {0, -sqrt(2), -sqrt(8)}, {sqrt(0.5), -sqrt(0.5), -sqrt(4.5)} },
  { { 1, 1, 1}, {0, -sqrt(2), -sqrt(8)}, {0, -sqrt(2), -sqrt(2)} },
  { { 1, 1, 0}, {0, -sqrt(2), 1}, {-sqrt(0.5), -sqrt(0.5), 1} },
  { { 1, 1, 0}, {0, -sqrt(2), 1}, {sqrt(0.5), -sqrt(0.5), 1} },
  { { 1, 1, 0}, {0, -sqrt(2), 1}, {0, -sqrt(2), 0} },
  { { 1, 1, 1}, {-sqrt(2), 0, -sqrt(8)}, {-sqrt(0.5), -sqrt(0.5), -sqrt(4.5)} },
  { { 1, 1, 1}, {-sqrt(2), 0, -sqrt(8)}, {-sqrt(0.5), sqrt(0.5), -sqrt(4.5)} },
  { { 1, 1, 1}, {-sqrt(2), 0, -sqrt(8)}, {-sqrt(2), 0, -sqrt(2)} },
  { { 0, 0, 0}, {1+sqrt(2), 1+sqrt(8), 1}, {1+sqrt(2), 1+sqrt(2), 1} },
  { { 0, 0, 0}, {1+sqrt(2), 1+sqrt(8), 1}, {sqrt(2), sqrt(8), 0} },
  { { 0, 0, 0}, {1+sqrt(2), 1+sqrt(8), 1}, {1, 1+sqrt(2), 1} },
  { { 1, 1, 0}, {-sqrt(2), 0, 1}, {-sqrt(0.5), -sqrt(0.5), 1} },
  { { 1, 1, 0}, {-sqrt(2), 0, 1}, {-sqrt(0.5), sqrt(0.5), 1} },
  { { 1, 1, 0}, {-sqrt(2), 0, 1}, {-sqrt(2), 0, 0} },
  { { 0, 2, 0}, {1+sqrt(2), -(1+sqrt(8)), 1}, {1+sqrt(2), -(1+sqrt(2)), 1} },
  { { 0, 2, 0}, {1+sqrt(2), -(1+sqrt(8)), 1}, {sqrt(2), -sqrt(8), 0} },
  { { 0, 2, 0}, {1+sqrt(2), -(1+sqrt(8)), 1}, {1, -(1+sqrt(2)), 1} },
  { { 1, 1, 1}, {sqrt(2), 0, -sqrt(8)}, {sqrt(0.5), -sqrt(0.5), -sqrt(4.5)} },
  { { 1, 1, 1}, {sqrt(2), 0, -sqrt(8)}, {sqrt(0.5), sqrt(0.5), -sqrt(4.5)} },
  { { 1, 1, 1}, {sqrt(2), 0, -sqrt(8)}, {sqrt(2), 0, -sqrt(2)} },
  { { 1, 1, 0}, {sqrt(2), 0, 1}, {sqrt(0.5), -sqrt(0.5), 1} },
  { { 1, 1, 0}, {sqrt(2), 0, 1}, {sqrt(0.5), sqrt(0.5), 1} },
  { { 1, 1, 0}, {sqrt(2), 0, 1}, {sqrt(2), 0, 0} },
  { { 2, 0, 0}, {-(1+sqrt(2)), 1+sqrt(8), 1}, {-(1+sqrt(2)), 1+sqrt(2), 1} },
  { { 2, 0, 0}, {-(1+sqrt(2)), 1+sqrt(8), 1}, {-sqrt(2), sqrt(8), 0} },
  { { 2, 0, 0}, {-(1+sqrt(2)), 1+sqrt(8), 1}, {-1, 1+sqrt(2), 1} },
  { { 2, 2, 0}, {-(1+sqrt(2)), -(1+sqrt(8)), 1}, {-(1+sqrt(2)), -(1+sqrt(2)), 1} },
  { { 2, 2, 0}, {-(1+sqrt(2)), -(1+sqrt(8)), 1}, {-sqrt(2), -sqrt(8), 0} },
  { { 2, 2, 0}, {-(1+sqrt(2)), -(1+sqrt(8)), 1}, {-1, -(1+sqrt(2)), 1} },
  { { 1, 1, 1}, {0, sqrt(2), -sqrt(8)}, {-sqrt(0.5), sqrt(0.5), -sqrt(4.5)} },
  { { 1, 1, 1}, {0, sqrt(2), -sqrt(8)}, {sqrt(0.5), sqrt(0.5), -sqrt(4.5)} },
  { { 1, 1, 1}, {0, sqrt(2), -sqrt(8)}, {0, sqrt(2), -sqrt(2)} },
  { { 0, 2, 0}, {1+sqrt(8), -(1+sqrt(2)), 1}, {1+sqrt(2), -(1+sqrt(2)), 1} },
  { { 0, 2, 0}, {1+sqrt(8), -(1+sqrt(2)), 1}, {sqrt(8), -sqrt(2), 0} },
  { { 0, 2, 0}, {1+sqrt(8), -(1+sqrt(2)), 1}, {1+sqrt(2), -1, 1} },
  { { 1, 1, 0}, {0, sqrt(2), 1}, {-sqrt(0.5), sqrt(0.5), 1} },
  { { 1, 1, 0}, {0, sqrt(2), 1}, {sqrt(0.5), sqrt(0.5), 1} },
  { { 1, 1, 0}, {0, sqrt(2), 1}, {0, sqrt(2), 0} },
  { { 2, 2, 0}, {-(1+sqrt(8)), -(1+sqrt(2)), 1}, {-(1+sqrt(2)), -(1+sqrt(2)), 1} },
  { { 2, 2, 0}, {-(1+sqrt(8)), -(1+sqrt(2)), 1}, {-sqrt(8), -sqrt(2), 0} },
  { { 2, 2, 0}, {-(1+sqrt(8)), -(1+sqrt(2)), 1}, {-(1+sqrt(2)), -1, 1} },
  { { 1, 1, 1}, {0, -sqrt(8), -sqrt(2)}, {-sqrt(0.5), -sqrt(4.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {0, -sqrt(8), -sqrt(2)}, {sqrt(0.5), -sqrt(4.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {0, -sqrt(8), -sqrt(2)}, {0, -sqrt(2), -sqrt(2)} },
  { { 0, 0, 0}, {1+sqrt(8), 1, 1+sqrt(2)}, {1+sqrt(2), 1, 1+sqrt(2)} },
  { { 0, 0, 0}, {1+sqrt(8), 1, 1+sqrt(2)}, {sqrt(8), 0, sqrt(2)} },
  { { 0, 0, 0}, {1+sqrt(8), 1, 1+sqrt(2)}, {1+sqrt(2), 1, 1} },
  { { 1, 0, 1}, {0, 1, -sqrt(2)}, {-sqrt(0.5), 1, -sqrt(0.5)} },
  { { 1, 0, 1}, {0, 1, -sqrt(2)}, {sqrt(0.5), 1, -sqrt(0.5)} },
  { { 1, 0, 1}, {0, 1, -sqrt(2)}, {0, 0, -sqrt(2)} },
  { { 2, 0, 0}, {-(1+sqrt(8)), 1, 1+sqrt(2)}, {-(1+sqrt(2)), 1, 1+sqrt(2)} },
  { { 2, 0, 0}, {-(1+sqrt(8)), 1, 1+sqrt(2)}, {-sqrt(8), 0, sqrt(2)} },
  { { 2, 0, 0}, {-(1+sqrt(8)), 1, 1+sqrt(2)}, {-(1+sqrt(2)), 1, 1} },
  { { 1, 1, 1}, {-sqrt(8), 0, -sqrt(2)}, {-sqrt(4.5), -sqrt(0.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(8), 0, -sqrt(2)}, {-sqrt(4.5), sqrt(0.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(8), 0, -sqrt(2)}, {-sqrt(2), 0, -sqrt(2)} },
  { { 0, 1, 1}, {1, 0, -sqrt(2)}, {1, -sqrt(0.5), -sqrt(0.5)} },
  { { 0, 1, 1}, {1, 0, -sqrt(2)}, {1, sqrt(0.5), -sqrt(0.5)} },
  { { 0, 1, 1}, {1, 0, -sqrt(2)}, {0, 0, -sqrt(2)} },
  { { 0, 0, 0}, {1, 1+sqrt(8), 1+sqrt(2)}, {1, 1+sqrt(2), 1+sqrt(2)} },
  { { 0, 0, 0}, {1, 1+sqrt(8), 1+sqrt(2)}, {0, sqrt(8), sqrt(2)} },
  { { 0, 0, 0}, {1, 1+sqrt(8), 1+sqrt(2)}, {1, 1+sqrt(2), 1} },
  { { 0, 2, 0}, {1, -(1+sqrt(8)), 1+sqrt(2)}, {1, -(1+sqrt(2)), 1+sqrt(2)} },
  { { 0, 2, 0}, {1, -(1+sqrt(8)), 1+sqrt(2)}, {0, -sqrt(8), sqrt(2)} },
  { { 0, 2, 0}, {1, -(1+sqrt(8)), 1+sqrt(2)}, {1, -(1+sqrt(2)), 1} },
  { { 1, 1, 1}, {sqrt(8), 0, -sqrt(2)}, {sqrt(4.5), -sqrt(0.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(8), 0, -sqrt(2)}, {sqrt(4.5), sqrt(0.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(8), 0, -sqrt(2)}, {sqrt(2), 0, -sqrt(2)} },
  { { 2, 0, 0}, {-1, 1+sqrt(8), 1+sqrt(2)}, {-1, 1+sqrt(2), 1+sqrt(2)} },
  { { 2, 0, 0}, {-1, 1+sqrt(8), 1+sqrt(2)}, {0, sqrt(8), sqrt(2)} },
  { { 2, 0, 0}, {-1, 1+sqrt(8), 1+sqrt(2)}, {-1, 1+sqrt(2), 1} },
  { { 2, 1, 1}, {-1, 0, -sqrt(2)}, {-1, -sqrt(0.5), -sqrt(0.5)} },
  { { 2, 1, 1}, {-1, 0, -sqrt(2)}, {-1, sqrt(0.5), -sqrt(0.5)} },
  { { 2, 1, 1}, {-1, 0, -sqrt(2)}, {0, 0, -sqrt(2)} },
  { { 2, 2, 0}, {-1, -(1+sqrt(8)), 1+sqrt(2)}, {-1, -(1+sqrt(2)), 1+sqrt(2)} },
  { { 2, 2, 0}, {-1, -(1+sqrt(8)), 1+sqrt(2)}, {0, -sqrt(8), sqrt(2)} },
  { { 2, 2, 0}, {-1, -(1+sqrt(8)), 1+sqrt(2)}, {-1, -(1+sqrt(2)), 1} },
  { { 1, 1, 1}, {0, sqrt(8), -sqrt(2)}, {-sqrt(0.5), sqrt(4.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {0, sqrt(8), -sqrt(2)}, {sqrt(0.5), sqrt(4.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {0, sqrt(8), -sqrt(2)}, {0, sqrt(2), -sqrt(2)} },
  { { 1, 2, 1}, {0, -1, -sqrt(2)}, {-sqrt(0.5), -1, -sqrt(0.5)} },
  { { 1, 2, 1}, {0, -1, -sqrt(2)}, {sqrt(0.5), -1, -sqrt(0.5)} },
  { { 1, 2, 1}, {0, -1, -sqrt(2)}, {0, 0, -sqrt(2)} },
  { { 0, 2, 0}, {1+sqrt(8), -1, 1+sqrt(2)}, {1+sqrt(2), -1, 1+sqrt(2)} },
  { { 0, 2, 0}, {1+sqrt(8), -1, 1+sqrt(2)}, {sqrt(8), 0, sqrt(2)} },
  { { 0, 2, 0}, {1+sqrt(8), -1, 1+sqrt(2)}, {1+sqrt(2), -1, 1} },
  { { 2, 2, 0}, {-(1+sqrt(8)), -1, 1+sqrt(2)}, {-(1+sqrt(2)), -1, 1+sqrt(2)} },
  { { 2, 2, 0}, {-(1+sqrt(8)), -1, 1+sqrt(2)}, {-sqrt(8), 0, sqrt(2)} },
  { { 2, 2, 0}, {-(1+sqrt(8)), -1, 1+sqrt(2)}, {-(1+sqrt(2)), -1, 1} },
  { { 1, 1, 1}, {-sqrt(2), -sqrt(8), 0}, {-sqrt(0.5), -sqrt(4.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(2), -sqrt(8), 0}, {-sqrt(0.5), -sqrt(4.5), sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(2), -sqrt(8), 0}, {-sqrt(2), -sqrt(2), 0} },
  { { 1, 0, 1}, {-sqrt(2), 1, 0}, {-sqrt(0.5), 1, -sqrt(0.5)} },
  { { 1, 0, 1}, {-sqrt(2), 1, 0}, {-sqrt(0.5), 1, sqrt(0.5)} },
  { { 1, 0, 1}, {-sqrt(2), 1, 0}, {-sqrt(2), 0, 0} },
  { { 0, 0, 0}, {1+sqrt(2), 1, 1+sqrt(8)}, {1+sqrt(2), 1, 1+sqrt(2)} },
  { { 0, 0, 0}, {1+sqrt(2), 1, 1+sqrt(8)}, {sqrt(2), 0, sqrt(8)} },
  { { 0, 0, 0}, {1+sqrt(2), 1, 1+sqrt(8)}, {1, 1, 1+sqrt(2)} },
  { { 0, 0, 2}, {1+sqrt(2), 1, -(1+sqrt(8))}, {1+sqrt(2), 1, -(1+sqrt(2))} },
  { { 0, 0, 2}, {1+sqrt(2), 1, -(1+sqrt(8))}, {sqrt(2), 0, -sqrt(8)} },
  { { 0, 0, 2}, {1+sqrt(2), 1, -(1+sqrt(8))}, {1, 1, -(1+sqrt(2))} },
  { { 1, 1, 1}, {sqrt(2), -sqrt(8), 0}, {sqrt(0.5), -sqrt(4.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(2), -sqrt(8), 0}, {sqrt(0.5), -sqrt(4.5), sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(2), -sqrt(8), 0}, {sqrt(2), -sqrt(2), 0} },
  { { 2, 0, 0}, {-(1+sqrt(2)), 1, 1+sqrt(8)}, {-(1+sqrt(2)), 1, 1+sqrt(2)} },
  { { 2, 0, 0}, {-(1+sqrt(2)), 1, 1+sqrt(8)}, {-sqrt(2), 0, sqrt(8)} },
  { { 2, 0, 0}, {-(1+sqrt(2)), 1, 1+sqrt(8)}, {-1, 1, 1+sqrt(2)} },
  { { 1, 0, 1}, {sqrt(2), 1, 0}, {sqrt(0.5), 1, -sqrt(0.5)} },
  { { 1, 0, 1}, {sqrt(2), 1, 0}, {sqrt(0.5), 1, sqrt(0.5)} },
  { { 1, 0, 1}, {sqrt(2), 1, 0}, {sqrt(2), 0, 0} },
  { { 2, 0, 2}, {-(1+sqrt(2)), 1, -(1+sqrt(8))}, {-(1+sqrt(2)), 1, -(1+sqrt(2))} },
  { { 2, 0, 2}, {-(1+sqrt(2)), 1, -(1+sqrt(8))}, {-sqrt(2), 0, -sqrt(8)} },
  { { 2, 0, 2}, {-(1+sqrt(2)), 1, -(1+sqrt(8))}, {-1, 1, -(1+sqrt(2))} },
  { { 1, 1, 1}, {-sqrt(8), -sqrt(2), 0}, {-sqrt(4.5), -sqrt(0.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(8), -sqrt(2), 0}, {-sqrt(4.5), -sqrt(0.5), sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(8), -sqrt(2), 0}, {-sqrt(2), -sqrt(2), 0} },
  { { 0, 0, 0}, {1, 1+sqrt(2), 1+sqrt(8)}, {1, 1+sqrt(2), 1+sqrt(2)} },
  { { 0, 0, 0}, {1, 1+sqrt(2), 1+sqrt(8)}, {0, sqrt(2), sqrt(8)} },
  { { 0, 0, 0}, {1, 1+sqrt(2), 1+sqrt(8)}, {1, 1, 1+sqrt(2)} },
  { { 0, 1, 1}, {1, -sqrt(2), 0}, {1, -sqrt(0.5), -sqrt(0.5)} },
  { { 0, 1, 1}, {1, -sqrt(2), 0}, {1, -sqrt(0.5), sqrt(0.5)} },
  { { 0, 1, 1}, {1, -sqrt(2), 0}, {0, -sqrt(2), 0} },
  { { 0, 0, 2}, {1, 1+sqrt(2), -(1+sqrt(8))}, {1, 1+sqrt(2), -(1+sqrt(2))} },
  { { 0, 0, 2}, {1, 1+sqrt(2), -(1+sqrt(8))}, {0, sqrt(2), -sqrt(8)} },
  { { 0, 0, 2}, {1, 1+sqrt(2), -(1+sqrt(8))}, {1, 1, -(1+sqrt(2))} },
  { { 1, 1, 1}, {sqrt(8), -sqrt(2), 0}, {sqrt(4.5), -sqrt(0.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(8), -sqrt(2), 0}, {sqrt(4.5), -sqrt(0.5), sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(8), -sqrt(2), 0}, {sqrt(2), -sqrt(2), 0} },
  { { 2, 1, 1}, {-1, -sqrt(2), 0}, {-1, -sqrt(0.5), -sqrt(0.5)} },
  { { 2, 1, 1}, {-1, -sqrt(2), 0}, {-1, -sqrt(0.5), sqrt(0.5)} },
  { { 2, 1, 1}, {-1, -sqrt(2), 0}, {0, -sqrt(2), 0} },
  { { 2, 0, 0}, {-1, 1+sqrt(2), 1+sqrt(8)}, {-1, 1+sqrt(2), 1+sqrt(2)} },
  { { 2, 0, 0}, {-1, 1+sqrt(2), 1+sqrt(8)}, {0, sqrt(2), sqrt(8)} },
  { { 2, 0, 0}, {-1, 1+sqrt(2), 1+sqrt(8)}, {-1, 1, 1+sqrt(2)} },
  { { 2, 0, 2}, {-1, 1+sqrt(2), -(1+sqrt(8))}, {-1, 1+sqrt(2), -(1+sqrt(2))} },
  { { 2, 0, 2}, {-1, 1+sqrt(2), -(1+sqrt(8))}, {0, sqrt(2), -sqrt(8)} },
  { { 2, 0, 2}, {-1, 1+sqrt(2), -(1+sqrt(8))}, {-1, 1, -(1+sqrt(2))} },
  { { 1, 1, 1}, {-sqrt(8), sqrt(2), 0}, {-sqrt(4.5), sqrt(0.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(8), sqrt(2), 0}, {-sqrt(4.5), sqrt(0.5), sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(8), sqrt(2), 0}, {-sqrt(2), sqrt(2), 0} },
  { { 0, 1, 1}, {1, sqrt(2), 0}, {1, sqrt(0.5), -sqrt(0.5)} },
  { { 0, 1, 1}, {1, sqrt(2), 0}, {1, sqrt(0.5), sqrt(0.5)} },
  { { 0, 1, 1}, {1, sqrt(2), 0}, {0, sqrt(2), 0} },
  { { 0, 2, 0}, {1, -(1+sqrt(2)), 1+sqrt(8)}, {1, -(1+sqrt(2)), 1+sqrt(2)} },
  { { 0, 2, 0}, {1, -(1+sqrt(2)), 1+sqrt(8)}, {0, -sqrt(2), sqrt(8)} },
  { { 0, 2, 0}, {1, -(1+sqrt(2)), 1+sqrt(8)}, {1, -1, 1+sqrt(2)} },
  { { 0, 2, 2}, {1, -(1+sqrt(2)), -(1+sqrt(8))}, {1, -(1+sqrt(2)), -(1+sqrt(2))} },
  { { 0, 2, 2}, {1, -(1+sqrt(2)), -(1+sqrt(8))}, {0, -sqrt(2), -sqrt(8)} },
  { { 0, 2, 2}, {1, -(1+sqrt(2)), -(1+sqrt(8))}, {1, -1, -(1+sqrt(2))} },
  { { 1, 1, 1}, {sqrt(8), sqrt(2), 0}, {sqrt(4.5), sqrt(0.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(8), sqrt(2), 0}, {sqrt(4.5), sqrt(0.5), sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(8), sqrt(2), 0}, {sqrt(2), sqrt(2), 0} },
  { { 2, 2, 0}, {-1, -(1+sqrt(2)), 1+sqrt(8)}, {-1, -(1+sqrt(2)), 1+sqrt(2)} },
  { { 2, 2, 0}, {-1, -(1+sqrt(2)), 1+sqrt(8)}, {0, -sqrt(2), sqrt(8)} },
  { { 2, 2, 0}, {-1, -(1+sqrt(2)), 1+sqrt(8)}, {-1, -1, 1+sqrt(2)} },
  { { 2, 1, 1}, {-1, sqrt(2), 0}, {-1, sqrt(0.5), -sqrt(0.5)} },
  { { 2, 1, 1}, {-1, sqrt(2), 0}, {-1, sqrt(0.5), sqrt(0.5)} },
  { { 2, 1, 1}, {-1, sqrt(2), 0}, {0, sqrt(2), 0} },
  { { 2, 2, 2}, {-1, -(1+sqrt(2)), -(1+sqrt(8))}, {-1, -(1+sqrt(2)), -(1+sqrt(2))} },
  { { 2, 2, 2}, {-1, -(1+sqrt(2)), -(1+sqrt(8))}, {0, -sqrt(2), -sqrt(8)} },
  { { 2, 2, 2}, {-1, -(1+sqrt(2)), -(1+sqrt(8))}, {-1, -1, -(1+sqrt(2))} },
  { { 1, 1, 1}, {-sqrt(2), sqrt(8), 0}, {-sqrt(0.5), sqrt(4.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(2), sqrt(8), 0}, {-sqrt(0.5), sqrt(4.5), sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(2), sqrt(8), 0}, {-sqrt(2), sqrt(2), 0} },
  { { 0, 2, 0}, {1+sqrt(2), -1, 1+sqrt(8)}, {1+sqrt(2), -1, 1+sqrt(2)} },
  { { 0, 2, 0}, {1+sqrt(2), -1, 1+sqrt(8)}, {sqrt(2), 0, sqrt(8)} },
  { { 0, 2, 0}, {1+sqrt(2), -1, 1+sqrt(8)}, {1, -1, 1+sqrt(2)} },
  { { 1, 2, 1}, {-sqrt(2), -1, 0}, {-sqrt(0.5), -1, -sqrt(0.5)} },
  { { 1, 2, 1}, {-sqrt(2), -1, 0}, {-sqrt(0.5), -1, sqrt(0.5)} },
  { { 1, 2, 1}, {-sqrt(2), -1, 0}, {-sqrt(2), 0, 0} },
  { { 0, 2, 2}, {1+sqrt(2), -1, -(1+sqrt(8))}, {1+sqrt(2), -1, -(1+sqrt(2))} },
  { { 0, 2, 2}, {1+sqrt(2), -1, -(1+sqrt(8))}, {sqrt(2), 0, -sqrt(8)} },
  { { 0, 2, 2}, {1+sqrt(2), -1, -(1+sqrt(8))}, {1, -1, -(1+sqrt(2))} },
  { { 1, 1, 1}, {sqrt(2), sqrt(8), 0}, {sqrt(0.5), sqrt(4.5), -sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(2), sqrt(8), 0}, {sqrt(0.5), sqrt(4.5), sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(2), sqrt(8), 0}, {sqrt(2), sqrt(2), 0} },
  { { 1, 2, 1}, {sqrt(2), -1, 0}, {sqrt(0.5), -1, -sqrt(0.5)} },
  { { 1, 2, 1}, {sqrt(2), -1, 0}, {sqrt(0.5), -1, sqrt(0.5)} },
  { { 1, 2, 1}, {sqrt(2), -1, 0}, {sqrt(2), 0, 0} },
  { { 2, 2, 0}, {-(1+sqrt(2)), -1, 1+sqrt(8)}, {-(1+sqrt(2)), -1, 1+sqrt(2)} },
  { { 2, 2, 0}, {-(1+sqrt(2)), -1, 1+sqrt(8)}, {-sqrt(2), 0, sqrt(8)} },
  { { 2, 2, 0}, {-(1+sqrt(2)), -1, 1+sqrt(8)}, {-1, -1, 1+sqrt(2)} },
  { { 2, 2, 2}, {-(1+sqrt(2)), -1, -(1+sqrt(8))}, {-(1+sqrt(2)), -1, -(1+sqrt(2))} },
  { { 2, 2, 2}, {-(1+sqrt(2)), -1, -(1+sqrt(8))}, {-sqrt(2), 0, -sqrt(8)} },
  { { 2, 2, 2}, {-(1+sqrt(2)), -1, -(1+sqrt(8))}, {-1, -1, -(1+sqrt(2))} },
  { { 1, 1, 1}, {0, -sqrt(8), sqrt(2)}, {-sqrt(0.5), -sqrt(4.5), sqrt(0.5)} },
  { { 1, 1, 1}, {0, -sqrt(8), sqrt(2)}, {sqrt(0.5), -sqrt(4.5), sqrt(0.5)} },
  { { 1, 1, 1}, {0, -sqrt(8), sqrt(2)}, {0, -sqrt(2), sqrt(2)} },
  { { 1, 0, 1}, {0, 1, sqrt(2)}, {-sqrt(0.5), 1, sqrt(0.5)} },
  { { 1, 0, 1}, {0, 1, sqrt(2)}, {sqrt(0.5), 1, sqrt(0.5)} },
  { { 1, 0, 1}, {0, 1, sqrt(2)}, {0, 0, sqrt(2)} },
  { { 0, 0, 2}, {1+sqrt(8), 1, -(1+sqrt(2))}, {1+sqrt(2), 1, -(1+sqrt(2))} },
  { { 0, 0, 2}, {1+sqrt(8), 1, -(1+sqrt(2))}, {sqrt(8), 0, -sqrt(2)} },
  { { 0, 0, 2}, {1+sqrt(8), 1, -(1+sqrt(2))}, {1+sqrt(2), 1, -1} },
  { { 2, 0, 2}, {-(1+sqrt(8)), 1, -(1+sqrt(2))}, {-(1+sqrt(2)), 1, -(1+sqrt(2))} },
  { { 2, 0, 2}, {-(1+sqrt(8)), 1, -(1+sqrt(2))}, {-sqrt(8), 0, -sqrt(2)} },
  { { 2, 0, 2}, {-(1+sqrt(8)), 1, -(1+sqrt(2))}, {-(1+sqrt(2)), 1, -1} },
  { { 1, 1, 1}, {-sqrt(8), 0, sqrt(2)}, {-sqrt(4.5), -sqrt(0.5), sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(8), 0, sqrt(2)}, {-sqrt(4.5), sqrt(0.5), sqrt(0.5)} },
  { { 1, 1, 1}, {-sqrt(8), 0, sqrt(2)}, {-sqrt(2), 0, sqrt(2)} },
  { { 0, 0, 2}, {1, 1+sqrt(8), -(1+sqrt(2))}, {1, 1+sqrt(2), -(1+sqrt(2))} },
  { { 0, 0, 2}, {1, 1+sqrt(8), -(1+sqrt(2))}, {0, sqrt(8), -sqrt(2)} },
  { { 0, 0, 2}, {1, 1+sqrt(8), -(1+sqrt(2))}, {1, 1+sqrt(2), -1} },
  { { 0, 1, 1}, {1, 0, sqrt(2)}, {1, -sqrt(0.5), sqrt(0.5)} },
  { { 0, 1, 1}, {1, 0, sqrt(2)}, {1, sqrt(0.5), sqrt(0.5)} },
  { { 0, 1, 1}, {1, 0, sqrt(2)}, {0, 0, sqrt(2)} },
  { { 0, 2, 2}, {1, -(1+sqrt(8)), -(1+sqrt(2))}, {1, -(1+sqrt(2)), -(1+sqrt(2))} },
  { { 0, 2, 2}, {1, -(1+sqrt(8)), -(1+sqrt(2))}, {0, -sqrt(8), -sqrt(2)} },
  { { 0, 2, 2}, {1, -(1+sqrt(8)), -(1+sqrt(2))}, {1, -(1+sqrt(2)), -1} },
  { { 1, 1, 1}, {sqrt(8), 0, sqrt(2)}, {sqrt(4.5), -sqrt(0.5), sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(8), 0, sqrt(2)}, {sqrt(4.5), sqrt(0.5), sqrt(0.5)} },
  { { 1, 1, 1}, {sqrt(8), 0, sqrt(2)}, {sqrt(2), 0, sqrt(2)} },
  { { 2, 1, 1}, {-1, 0, sqrt(2)}, {-1, -sqrt(0.5), sqrt(0.5)} },
  { { 2, 1, 1}, {-1, 0, sqrt(2)}, {-1, sqrt(0.5), sqrt(0.5)} },
  { { 2, 1, 1}, {-1, 0, sqrt(2)}, {0, 0, sqrt(2)} },
  { { 2, 0, 2}, {-1, 1+sqrt(8), -(1+sqrt(2))}, {-1, 1+sqrt(2), -(1+sqrt(2))} },
  { { 2, 0, 2}, {-1, 1+sqrt(8), -(1+sqrt(2))}, {0, sqrt(8), -sqrt(2)} },
  { { 2, 0, 2}, {-1, 1+sqrt(8), -(1+sqrt(2))}, {-1, 1+sqrt(2), -1} },
  { { 2, 2, 2}, {-1, -(1+sqrt(8)), -(1+sqrt(2))}, {-1, -(1+sqrt(2)), -(1+sqrt(2))} },
  { { 2, 2, 2}, {-1, -(1+sqrt(8)), -(1+sqrt(2))}, {0, -sqrt(8), -sqrt(2)} },
  { { 2, 2, 2}, {-1, -(1+sqrt(8)), -(1+sqrt(2))}, {-1, -(1+sqrt(2)), -1} },
  { { 1, 1, 1}, {0, sqrt(8), sqrt(2)}, {-sqrt(0.5), sqrt(4.5), sqrt(0.5)} },
  { { 1, 1, 1}, {0, sqrt(8), sqrt(2)}, {sqrt(0.5), sqrt(4.5), sqrt(0.5)} },
  { { 1, 1, 1}, {0, sqrt(8), sqrt(2)}, {0, sqrt(2), sqrt(2)} },
  { { 0, 2, 2}, {1+sqrt(8), -1, -(1+sqrt(2))}, {1+sqrt(2), -1, -(1+sqrt(2))} },
  { { 0, 2, 2}, {1+sqrt(8), -1, -(1+sqrt(2))}, {sqrt(8), 0, -sqrt(2)} },
  { { 0, 2, 2}, {1+sqrt(8), -1, -(1+sqrt(2))}, {1+sqrt(2), -1, -1} },
  { { 1, 2, 1}, {0, -1, sqrt(2)}, {-sqrt(0.5), -1, sqrt(0.5)} },
  { { 1, 2, 1}, {0, -1, sqrt(2)}, {sqrt(0.5), -1, sqrt(0.5)} },
  { { 1, 2, 1}, {0, -1, sqrt(2)}, {0, 0, sqrt(2)} },
  { { 2, 2, 2}, {-(1+sqrt(8)), -1, -(1+sqrt(2))}, {-(1+sqrt(2)), -1, -(1+sqrt(2))} },
  { { 2, 2, 2}, {-(1+sqrt(8)), -1, -(1+sqrt(2))}, {-sqrt(8), 0, -sqrt(2)} },
  { { 2, 2, 2}, {-(1+sqrt(8)), -1, -(1+sqrt(2))}, {-(1+sqrt(2)), -1, -1} },
  { { 1, 1, 1}, {0, -sqrt(2), sqrt(8)}, {-sqrt(0.5), -sqrt(0.5), sqrt(4.5)} },
  { { 1, 1, 1}, {0, -sqrt(2), sqrt(8)}, {sqrt(0.5), -sqrt(0.5), sqrt(4.5)} },
  { { 1, 1, 1}, {0, -sqrt(2), sqrt(8)}, {0, -sqrt(2), sqrt(2)} },
  { { 0, 0, 2}, {1+sqrt(8), 1+sqrt(2), -1}, {1+sqrt(2), 1+sqrt(2), -1} },
  { { 0, 0, 2}, {1+sqrt(8), 1+sqrt(2), -1}, {sqrt(8), sqrt(2), 0} },
  { { 0, 0, 2}, {1+sqrt(8), 1+sqrt(2), -1}, {1+sqrt(2), 1, -1} },
  { { 1, 1, 2}, {0, -sqrt(2), -1}, {-sqrt(0.5), -sqrt(0.5), -1} },
  { { 1, 1, 2}, {0, -sqrt(2), -1}, {sqrt(0.5), -sqrt(0.5), -1} },
  { { 1, 1, 2}, {0, -sqrt(2), -1}, {0, -sqrt(2), 0} },
  { { 2, 0, 2}, {-(1+sqrt(8)), 1+sqrt(2), -1}, {-(1+sqrt(2)), 1+sqrt(2), -1} },
  { { 2, 0, 2}, {-(1+sqrt(8)), 1+sqrt(2), -1}, {-sqrt(8), sqrt(2), 0} },
  { { 2, 0, 2}, {-(1+sqrt(8)), 1+sqrt(2), -1}, {-(1+sqrt(2)), 1, -1} },
  { { 1, 1, 1}, {-sqrt(2), 0, sqrt(8)}, {-sqrt(0.5), -sqrt(0.5), sqrt(4.5)} },
  { { 1, 1, 1}, {-sqrt(2), 0, sqrt(8)}, {-sqrt(0.5), sqrt(0.5), sqrt(4.5)} },
  { { 1, 1, 1}, {-sqrt(2), 0, sqrt(8)}, {-sqrt(2), 0, sqrt(2)} },
  { { 1, 1, 2}, {-sqrt(2), 0, -1}, {-sqrt(0.5), -sqrt(0.5), -1} },
  { { 1, 1, 2}, {-sqrt(2), 0, -1}, {-sqrt(0.5), sqrt(0.5), -1} },
  { { 1, 1, 2}, {-sqrt(2), 0, -1}, {-sqrt(2), 0, 0} },
  { { 0, 0, 2}, {1+sqrt(2), 1+sqrt(8), -1}, {1+sqrt(2), 1+sqrt(2), -1} },
  { { 0, 0, 2}, {1+sqrt(2), 1+sqrt(8), -1}, {sqrt(2), sqrt(8), 0} },
  { { 0, 0, 2}, {1+sqrt(2), 1+sqrt(8), -1}, {1, 1+sqrt(2), -1} },
  { { 0, 2, 2}, {1+sqrt(2), -(1+sqrt(8)), -1}, {1+sqrt(2), -(1+sqrt(2)), -1} },
  { { 0, 2, 2}, {1+sqrt(2), -(1+sqrt(8)), -1}, {sqrt(2), -sqrt(8), 0} },
  { { 0, 2, 2}, {1+sqrt(2), -(1+sqrt(8)), -1}, {1, -(1+sqrt(2)), -1} },
  { { 1, 1, 1}, {sqrt(2), 0, sqrt(8)}, {sqrt(0.5), -sqrt(0.5), sqrt(4.5)} },
  { { 1, 1, 1}, {sqrt(2), 0, sqrt(8)}, {sqrt(0.5), sqrt(0.5), sqrt(4.5)} },
  { { 1, 1, 1}, {sqrt(2), 0, sqrt(8)}, {sqrt(2), 0, sqrt(2)} },
  { { 2, 0, 2}, {-(1+sqrt(2)), 1+sqrt(8), -1}, {-(1+sqrt(2)), 1+sqrt(2), -1} },
  { { 2, 0, 2}, {-(1+sqrt(2)), 1+sqrt(8), -1}, {-sqrt(2), sqrt(8), 0} },
  { { 2, 0, 2}, {-(1+sqrt(2)), 1+sqrt(8), -1}, {-1, 1+sqrt(2), -1} },
  { { 1, 1, 2}, {sqrt(2), 0, -1}, {sqrt(0.5), -sqrt(0.5), -1} },
  { { 1, 1, 2}, {sqrt(2), 0, -1}, {sqrt(0.5), sqrt(0.5), -1} },
  { { 1, 1, 2}, {sqrt(2), 0, -1}, {sqrt(2), 0, 0} },
  { { 2, 2, 2}, {-(1+sqrt(2)), -(1+sqrt(8)), -1}, {-(1+sqrt(2)), -(1+sqrt(2)), -1} },
  { { 2, 2, 2}, {-(1+sqrt(2)), -(1+sqrt(8)), -1}, {-sqrt(2), -sqrt(8), 0} },
  { { 2, 2, 2}, {-(1+sqrt(2)), -(1+sqrt(8)), -1}, {-1, -(1+sqrt(2)), -1} },
  { { 1, 1, 1}, {0, sqrt(2), sqrt(8)}, {-sqrt(0.5), sqrt(0.5), sqrt(4.5)} },
  { { 1, 1, 1}, {0, sqrt(2), sqrt(8)}, {sqrt(0.5), sqrt(0.5), sqrt(4.5)} },
  { { 1, 1, 1}, {0, sqrt(2), sqrt(8)}, {0, sqrt(2), sqrt(2)} },
  { { 1, 1, 2}, {0, sqrt(2), -1}, {-sqrt(0.5), sqrt(0.5), -1} },
  { { 1, 1, 2}, {0, sqrt(2), -1}, {sqrt(0.5), sqrt(0.5), -1} },
  { { 1, 1, 2}, {0, sqrt(2), -1}, {0, sqrt(2), 0} },
  { { 0, 2, 2}, {1+sqrt(8), -(1+sqrt(2)), -1}, {1+sqrt(2), -(1+sqrt(2)), -1} },
  { { 0, 2, 2}, {1+sqrt(8), -(1+sqrt(2)), -1}, {sqrt(8), -sqrt(2), 0} },
  { { 0, 2, 2}, {1+sqrt(8), -(1+sqrt(2)), -1}, {1+sqrt(2), -1, -1} },
  { { 2, 2, 2}, {-(1+sqrt(8)), -(1+sqrt(2)), -1}, {-(1+sqrt(2)), -(1+sqrt(2)), -1} },
  { { 2, 2, 2}, {-(1+sqrt(8)), -(1+sqrt(2)), -1}, {-sqrt(8), -sqrt(2), 0} },
  { { 2, 2, 2}, {-(1+sqrt(8)), -(1+sqrt(2)), -1}, {-(1+sqrt(2)), -1, -1} },
};

static const int normalFaces[24][4][3] = {
  {
    { 6, 9, 0 },
    { 7, 3, 10 },
    { 11, 4, 1 },
    { 2, 5, 8 },
  },
  {
    { 12, 15, 18 },
    { 13, 19, 21 },
    { 20, 16, 22 },
    { 17, 14, 23 },
  },
  {
    { 24, 27, 30 },
    { 25, 33, 28 },
    { 29, 34, 31 },
    { 32, 35, 26 },
  },
  {
    { 36, 39, 42 },
    { 37, 43, 45 },
    { 44, 40, 46 },
    { 41, 38, 47 },
  },
  {
    { 48, 51, 54 },
    { 49, 55, 57 },
    { 56, 52, 58 },
    { 53, 50, 59 },
  },
  {
    { 60, 63, 66 },
    { 61, 69, 64 },
    { 65, 70, 67 },
    { 68, 71, 62 },
  },
  {
    { 72, 75, 78 },
    { 73, 79, 81 },
    { 80, 76, 82 },
    { 77, 74, 83 },
  },
  {
    { 84, 87, 90 },
    { 85, 93, 88 },
    { 89, 94, 91 },
    { 92, 95, 86 },
  },
  {
    { 96, 99, 102 },
    { 97, 105, 100 },
    { 101, 106, 103 },
    { 104, 107, 98 },
  },
  {
    { 108, 111, 114 },
    { 109, 115, 117 },
    { 116, 112, 118 },
    { 113, 110, 119 },
  },
  {
    { 120, 123, 126 },
    { 121, 127, 129 },
    { 128, 124, 130 },
    { 125, 122, 131 },
  },
  {
    { 132, 135, 138 },
    { 133, 141, 136 },
    { 137, 142, 139 },
    { 140, 143, 134 },
  },
  {
    { 144, 147, 150 },
    { 145, 153, 148 },
    { 149, 154, 151 },
    { 152, 155, 146 },
  },
  {
    { 156, 159, 162 },
    { 157, 163, 165 },
    { 164, 160, 166 },
    { 161, 158, 167 },
  },
  {
    { 168, 171, 174 },
    { 169, 175, 177 },
    { 176, 172, 178 },
    { 173, 170, 179 },
  },
  {
    { 180, 183, 186 },
    { 181, 189, 184 },
    { 185, 190, 187 },
    { 188, 191, 182 },
  },
  {
    { 192, 195, 198 },
    { 193, 201, 196 },
    { 197, 202, 199 },
    { 200, 203, 194 },
  },
  {
    { 204, 207, 210 },
    { 205, 211, 213 },
    { 212, 208, 214 },
    { 209, 206, 215 },
  },
  {
    { 216, 219, 222 },
    { 217, 225, 220 },
    { 221, 226, 223 },
    { 224, 227, 218 },
  },
  {
    { 228, 231, 234 },
    { 229, 235, 237 },
    { 236, 232, 238 },
    { 233, 230, 239 },
  },
  {
    { 240, 243, 246 },
    { 241, 247, 249 },
    { 248, 244, 250 },
    { 245, 242, 251 },
  },
  {
    { 252, 255, 258 },
    { 253, 261, 256 },
    { 257, 262, 259 },
    { 260, 263, 254 },
  },
  {
    { 264, 267, 270 },
    { 265, 271, 273 },
    { 272, 268, 274 },
    { 269, 266, 275 },
  },
  {
    { 276, 279, 282 },
    { 277, 285, 280 },
    { 281, 286, 283 },
    { 284, 287, 278 },
  },
};

static const int bevelFaces[24][10][5] = {
  {
    { 4,  1, 4, 5, 2 },
    { 4,  6, 0, 2, 8 },
    { 4,  0, 9, 11, 1 },
    { 4,  3, 7, 8, 5 },
    { 4,  10, 3, 4, 11 },
    { 4,  9, 6, 7, 10 },
    { 3,  0, 1, 2 },
    { 3,  3, 5, 4 },
    { 3,  6, 8, 7 },
    { 3,  9, 10, 11 },
  },
  {
    { 4,  15, 12, 14, 17 },
    { 4,  12, 18, 19, 13 },
    { 4,  13, 21, 23, 14 },
    { 4,  18, 15, 16, 20 },
    { 4,  22, 16, 17, 23 },
    { 4,  21, 19, 20, 22 },
    { 3,  12, 13, 14 },
    { 3,  15, 17, 16 },
    { 3,  18, 20, 19 },
    { 3,  21, 22, 23 },
  },
  {
    { 4,  27, 24, 25, 28 },
    { 4,  24, 30, 32, 26 },
    { 4,  33, 25, 26, 35 },
    { 4,  30, 27, 29, 31 },
    { 4,  28, 33, 34, 29 },
    { 4,  31, 34, 35, 32 },
    { 3,  24, 26, 25 },
    { 3,  27, 28, 29 },
    { 3,  30, 31, 32 },
    { 3,  33, 35, 34 },
  },
  {
    { 4,  39, 36, 38, 41 },
    { 4,  36, 42, 43, 37 },
    { 4,  37, 45, 47, 38 },
    { 4,  42, 39, 40, 44 },
    { 4,  46, 40, 41, 47 },
    { 4,  45, 43, 44, 46 },
    { 3,  36, 37, 38 },
    { 3,  39, 41, 40 },
    { 3,  42, 44, 43 },
    { 3,  45, 46, 47 },
  },
  {
    { 4,  51, 48, 50, 53 },
    { 4,  48, 54, 55, 49 },
    { 4,  49, 57, 59, 50 },
    { 4,  54, 51, 52, 56 },
    { 4,  58, 52, 53, 59 },
    { 4,  57, 55, 56, 58 },
    { 3,  48, 49, 50 },
    { 3,  51, 53, 52 },
    { 3,  54, 56, 55 },
    { 3,  57, 58, 59 },
  },
  {
    { 4,  63, 60, 61, 64 },
    { 4,  60, 66, 68, 62 },
    { 4,  69, 61, 62, 71 },
    { 4,  66, 63, 65, 67 },
    { 4,  64, 69, 70, 65 },
    { 4,  67, 70, 71, 68 },
    { 3,  60, 62, 61 },
    { 3,  63, 64, 65 },
    { 3,  66, 67, 68 },
    { 3,  69, 71, 70 },
  },
  {
    { 4,  75, 72, 74, 77 },
    { 4,  72, 78, 79, 73 },
    { 4,  73, 81, 83, 74 },
    { 4,  78, 75, 76, 80 },
    { 4,  82, 76, 77, 83 },
    { 4,  81, 79, 80, 82 },
    { 3,  72, 73, 74 },
    { 3,  75, 77, 76 },
    { 3,  78, 80, 79 },
    { 3,  81, 82, 83 },
  },
  {
    { 4,  87, 84, 85, 88 },
    { 4,  84, 90, 92, 86 },
    { 4,  93, 85, 86, 95 },
    { 4,  90, 87, 89, 91 },
    { 4,  88, 93, 94, 89 },
    { 4,  91, 94, 95, 92 },
    { 3,  84, 86, 85 },
    { 3,  87, 88, 89 },
    { 3,  90, 91, 92 },
    { 3,  93, 95, 94 },
  },
  {
    { 4,  99, 96, 97, 100 },
    { 4,  96, 102, 104, 98 },
    { 4,  105, 97, 98, 107 },
    { 4,  102, 99, 101, 103 },
    { 4,  100, 105, 106, 101 },
    { 4,  103, 106, 107, 104 },
    { 3,  96, 98, 97 },
    { 3,  99, 100, 101 },
    { 3,  102, 103, 104 },
    { 3,  105, 107, 106 },
  },
  {
    { 4,  111, 108, 110, 113 },
    { 4,  108, 114, 115, 109 },
    { 4,  109, 117, 119, 110 },
    { 4,  114, 111, 112, 116 },
    { 4,  118, 112, 113, 119 },
    { 4,  117, 115, 116, 118 },
    { 3,  108, 109, 110 },
    { 3,  111, 113, 112 },
    { 3,  114, 116, 115 },
    { 3,  117, 118, 119 },
  },
  {
    { 4,  123, 120, 122, 125 },
    { 4,  120, 126, 127, 121 },
    { 4,  121, 129, 131, 122 },
    { 4,  126, 123, 124, 128 },
    { 4,  130, 124, 125, 131 },
    { 4,  129, 127, 128, 130 },
    { 3,  120, 121, 122 },
    { 3,  123, 125, 124 },
    { 3,  126, 128, 127 },
    { 3,  129, 130, 131 },
  },
  {
    { 4,  135, 132, 133, 136 },
    { 4,  132, 138, 140, 134 },
    { 4,  141, 133, 134, 143 },
    { 4,  138, 135, 137, 139 },
    { 4,  136, 141, 142, 137 },
    { 4,  139, 142, 143, 140 },
    { 3,  132, 134, 133 },
    { 3,  135, 136, 137 },
    { 3,  138, 139, 140 },
    { 3,  141, 143, 142 },
  },
  {
    { 4,  147, 144, 145, 148 },
    { 4,  144, 150, 152, 146 },
    { 4,  153, 145, 146, 155 },
    { 4,  150, 147, 149, 151 },
    { 4,  148, 153, 154, 149 },
    { 4,  151, 154, 155, 152 },
    { 3,  144, 146, 145 },
    { 3,  147, 148, 149 },
    { 3,  150, 151, 152 },
    { 3,  153, 155, 154 },
  },
  {
    { 4,  159, 156, 158, 161 },
    { 4,  156, 162, 163, 157 },
    { 4,  157, 165, 167, 158 },
    { 4,  162, 159, 160, 164 },
    { 4,  166, 160, 161, 167 },
    { 4,  165, 163, 164, 166 },
    { 3,  156, 157, 158 },
    { 3,  159, 161, 160 },
    { 3,  162, 164, 163 },
    { 3,  165, 166, 167 },
  },
  {
    { 4,  171, 168, 170, 173 },
    { 4,  168, 174, 175, 169 },
    { 4,  169, 177, 179, 170 },
    { 4,  174, 171, 172, 176 },
    { 4,  178, 172, 173, 179 },
    { 4,  177, 175, 176, 178 },
    { 3,  168, 169, 170 },
    { 3,  171, 173, 172 },
    { 3,  174, 176, 175 },
    { 3,  177, 178, 179 },
  },
  {
    { 4,  183, 180, 181, 184 },
    { 4,  180, 186, 188, 182 },
    { 4,  189, 181, 182, 191 },
    { 4,  186, 183, 185, 187 },
    { 4,  184, 189, 190, 185 },
    { 4,  187, 190, 191, 188 },
    { 3,  180, 182, 181 },
    { 3,  183, 184, 185 },
    { 3,  186, 187, 188 },
    { 3,  189, 191, 190 },
  },
  {
    { 4,  195, 192, 193, 196 },
    { 4,  192, 198, 200, 194 },
    { 4,  201, 193, 194, 203 },
    { 4,  198, 195, 197, 199 },
    { 4,  196, 201, 202, 197 },
    { 4,  199, 202, 203, 200 },
    { 3,  192, 194, 193 },
    { 3,  195, 196, 197 },
    { 3,  198, 199, 200 },
    { 3,  201, 203, 202 },
  },
  {
    { 4,  207, 204, 206, 209 },
    { 4,  204, 210, 211, 205 },
    { 4,  205, 213, 215, 206 },
    { 4,  210, 207, 208, 212 },
    { 4,  214, 208, 209, 215 },
    { 4,  213, 211, 212, 214 },
    { 3,  204, 205, 206 },
    { 3,  207, 209, 208 },
    { 3,  210, 212, 211 },
    { 3,  213, 214, 215 },
  },
  {
    { 4,  219, 216, 217, 220 },
    { 4,  216, 222, 224, 218 },
    { 4,  225, 217, 218, 227 },
    { 4,  222, 219, 221, 223 },
    { 4,  220, 225, 226, 221 },
    { 4,  223, 226, 227, 224 },
    { 3,  216, 218, 217 },
    { 3,  219, 220, 221 },
    { 3,  222, 223, 224 },
    { 3,  225, 227, 226 },
  },
  {
    { 4,  231, 228, 230, 233 },
    { 4,  228, 234, 235, 229 },
    { 4,  229, 237, 239, 230 },
    { 4,  234, 231, 232, 236 },
    { 4,  238, 232, 233, 239 },
    { 4,  237, 235, 236, 238 },
    { 3,  228, 229, 230 },
    { 3,  231, 233, 232 },
    { 3,  234, 236, 235 },
    { 3,  237, 238, 239 },
  },
  {
    { 4,  243, 240, 242, 245 },
    { 4,  240, 246, 247, 241 },
    { 4,  241, 249, 251, 242 },
    { 4,  246, 243, 244, 248 },
    { 4,  250, 244, 245, 251 },
    { 4,  249, 247, 248, 250 },
    { 3,  240, 241, 242 },
    { 3,  243, 245, 244 },
    { 3,  246, 248, 247 },
    { 3,  249, 250, 251 },
  },
  {
    { 4,  255, 252, 253, 256 },
    { 4,  252, 258, 260, 254 },
    { 4,  261, 253, 254, 263 },
    { 4,  258, 255, 257, 259 },
    { 4,  256, 261, 262, 257 },
    { 4,  259, 262, 263, 260 },
    { 3,  252, 254, 253 },
    { 3,  255, 256, 257 },
    { 3,  258, 259, 260 },
    { 3,  261, 263, 262 },
  },
  {
    { 4,  267, 264, 266, 269 },
    { 4,  264, 270, 271, 265 },
    { 4,  265, 273, 275, 266 },
    { 4,  270, 267, 268, 272 },
    { 4,  274, 268, 269, 275 },
    { 4,  273, 271, 272, 274 },
    { 3,  264, 265, 266 },
    { 3,  267, 269, 268 },
    { 3,  270, 272, 271 },
    { 3,  273, 274, 275 },
  },
  {
    { 4,  279, 276, 277, 280 },
    { 4,  276, 282, 284, 278 },
    { 4,  285, 277, 278, 287 },
    { 4,  282, 279, 281, 283 },
    { 4,  280, 285, 286, 281 },
    { 4,  283, 286, 287, 284 },
    { 3,  276, 278, 277 },
    { 3,  279, 280, 281 },
    { 3,  282, 283, 284 },
    { 3,  285, 287, 286 },
  },
};