static const double vertices[][3][3] = {
  { { 0, 0, 0}, {sqrt(3), sqrt(3), sqrt(3)}, {sqrt(3), sqrt(0.75), sqrt(0.75)} },
  { { 0, 0, 0}, {sqrt(3), sqrt(3), sqrt(3)}, {sqrt(0.75), sqrt(3), sqrt(0.75)} },
  { { 0, 0, 0}, {sqrt(3), sqrt(3), sqrt(3)}, {sqrt(0.75), sqrt(0.75), sqrt(3)} },
  { { 1, 1, 0}, {-sqrt(3), -sqrt(3), sqrt(3)}, {-sqrt(0.75), -sqrt(3), sqrt(0.75)} },
  { { 1, 1, 0}, {-sqrt(3), -sqrt(3), sqrt(3)}, {-sqrt(3), -sqrt(0.75), sqrt(0.75)} },
  { { 1, 1, 0}, {-sqrt(3), -sqrt(3), sqrt(3)}, {-sqrt(0.75), -sqrt(0.75), sqrt(3)} },
  { { 1, 0, 1}, {-sqrt(3), sqrt(3), -sqrt(3)}, {-sqrt(0.75), sqrt(0.75), -sqrt(3)} },
  { { 1, 0, 1}, {-sqrt(3), sqrt(3), -sqrt(3)}, {-sqrt(3), sqrt(0.75), -sqrt(0.75)} },
  { { 1, 0, 1}, {-sqrt(3), sqrt(3), -sqrt(3)}, {-sqrt(0.75), sqrt(3), -sqrt(0.75)} },
  { { 0, 1, 1}, {sqrt(3), -sqrt(3), -sqrt(3)}, {sqrt(0.75), -sqrt(0.75), -sqrt(3)} },
  { { 0, 1, 1}, {sqrt(3), -sqrt(3), -sqrt(3)}, {sqrt(0.75), -sqrt(3), -sqrt(0.75)} },
  { { 0, 1, 1}, {sqrt(3), -sqrt(3), -sqrt(3)}, {sqrt(3), -sqrt(0.75), -sqrt(0.75)} },
  { { 1, 0, 0}, {-sqrt(3), sqrt(3), sqrt(3)}, {-sqrt(3), sqrt(0.75), sqrt(0.75)} },
  { { 1, 0, 0}, {-sqrt(3), sqrt(3), sqrt(3)}, {-sqrt(0.75), sqrt(3), sqrt(0.75)} },
  { { 1, 0, 0}, {-sqrt(3), sqrt(3), sqrt(3)}, {-sqrt(0.75), sqrt(0.75), sqrt(3)} },
  { { 0, 0, 1}, {sqrt(3), sqrt(3), -sqrt(3)}, {sqrt(0.75), sqrt(0.75), -sqrt(3)} },
  { { 0, 0, 1}, {sqrt(3), sqrt(3), -sqrt(3)}, {sqrt(3), sqrt(0.75), -sqrt(0.75)} },
  { { 0, 0, 1}, {sqrt(3), sqrt(3), -sqrt(3)}, {sqrt(0.75), sqrt(3), -sqrt(0.75)} },
  { { 0, 1, 0}, {sqrt(3), -sqrt(3), sqrt(3)}, {sqrt(0.75), -sqrt(3), sqrt(0.75)} },
  { { 0, 1, 0}, {sqrt(3), -sqrt(3), sqrt(3)}, {sqrt(3), -sqrt(0.75), sqrt(0.75)} },
  { { 0, 1, 0}, {sqrt(3), -sqrt(3), sqrt(3)}, {sqrt(0.75), -sqrt(0.75), sqrt(3)} },
  { { 1, 1, 1}, {-sqrt(3), -sqrt(3), -sqrt(3)}, {-sqrt(0.75), -sqrt(0.75), -sqrt(3)} },
  { { 1, 1, 1}, {-sqrt(3), -sqrt(3), -sqrt(3)}, {-sqrt(0.75), -sqrt(3), -sqrt(0.75)} },
  { { 1, 1, 1}, {-sqrt(3), -sqrt(3), -sqrt(3)}, {-sqrt(3), -sqrt(0.75), -sqrt(0.75)} },
  { { 0, 0, 0}, {2+sqrt(3), 1, 1}, {2, 1, 1} },
  { { 0, 0, 0}, {2+sqrt(3), 1, 1}, {1+sqrt(3), 1, 0} },
  { { 0, 0, 0}, {2+sqrt(3), 1, 1}, {1+sqrt(3), 0, 1} },
  { { 1, 0, 1}, {-1, 1, -(2+sqrt(3))}, {-1, 1, -2} },
  { { 1, 0, 1}, {-1, 1, -(2+sqrt(3))}, {0, 1, -(1+sqrt(3))} },
  { { 1, 0, 1}, {-1, 1, -(2+sqrt(3))}, {-1, 0, -(1+sqrt(3))} },
  { { 1, 1, 0}, {-1, -(2+sqrt(3)), 1}, {-1, -2, 1} },
  { { 1, 1, 0}, {-1, -(2+sqrt(3)), 1}, {-1, -(1+sqrt(3)), 0} },
  { { 1, 1, 0}, {-1, -(2+sqrt(3)), 1}, {0, -(1+sqrt(3)), 1} },
  { { 1, 0, 0}, {-1, 1, 1}, {-1, 1, 0} },
  { { 1, 0, 0}, {-1, 1, 1}, {0, 1, 1} },
  { { 1, 0, 0}, {-1, 1, 1}, {-1, 0, 1} },
  { { 1, 0, 0}, {-(2+sqrt(3)), 1, 1}, {-2, 1, 1} },
  { { 1, 0, 0}, {-(2+sqrt(3)), 1, 1}, {-(1+sqrt(3)), 1, 0} },
  { { 1, 0, 0}, {-(2+sqrt(3)), 1, 1}, {-(1+sqrt(3)), 0, 1} },
  { { 0, 1, 0}, {1, -(2+sqrt(3)), 1}, {1, -2, 1} },
  { { 0, 1, 0}, {1, -(2+sqrt(3)), 1}, {1, -(1+sqrt(3)), 0} },
  { { 0, 1, 0}, {1, -(2+sqrt(3)), 1}, {0, -(1+sqrt(3)), 1} },
  { { 0, 0, 1}, {1, 1, -(2+sqrt(3))}, {1, 1, -2} },
  { { 0, 0, 1}, {1, 1, -(2+sqrt(3))}, {1, 0, -(1+sqrt(3))} },
  { { 0, 0, 1}, {1, 1, -(2+sqrt(3))}, {0, 1, -(1+sqrt(3))} },
  { { 0, 0, 0}, {1, 1, 1}, {1, 1, 0} },
  { { 0, 0, 0}, {1, 1, 1}, {1, 0, 1} },
  { { 0, 0, 0}, {1, 1, 1}, {0, 1, 1} },
  { { 0, 0, 0}, {1, 2+sqrt(3), 1}, {1, 2, 1} },
  { { 0, 0, 0}, {1, 2+sqrt(3), 1}, {1, 1+sqrt(3), 0} },
  { { 0, 0, 0}, {1, 2+sqrt(3), 1}, {0, 1+sqrt(3), 1} },
  { { 1, 1, 0}, {-(2+sqrt(3)), -1, 1}, {-2, -1, 1} },
  { { 1, 1, 0}, {-(2+sqrt(3)), -1, 1}, {-(1+sqrt(3)), -1, 0} },
  { { 1, 1, 0}, {-(2+sqrt(3)), -1, 1}, {-(1+sqrt(3)), 0, 1} },
  { { 0, 1, 1}, {1, -1, -(2+sqrt(3))}, {1, -1, -2} },
  { { 0, 1, 1}, {1, -1, -(2+sqrt(3))}, {1, 0, -(1+sqrt(3))} },
  { { 0, 1, 1}, {1, -1, -(2+sqrt(3))}, {0, -1, -(1+sqrt(3))} },
  { { 0, 1, 0}, {1, -1, 1}, {1, -1, 0} },
  { { 0, 1, 0}, {1, -1, 1}, {1, 0, 1} },
  { { 0, 1, 0}, {1, -1, 1}, {0, -1, 1} },
  { { 0, 1, 0}, {2+sqrt(3), -1, 1}, {2, -1, 1} },
  { { 0, 1, 0}, {2+sqrt(3), -1, 1}, {1+sqrt(3), -1, 0} },
  { { 0, 1, 0}, {2+sqrt(3), -1, 1}, {1+sqrt(3), 0, 1} },
  { { 1, 0, 0}, {-1, 2+sqrt(3), 1}, {-1, 2, 1} },
  { { 1, 0, 0}, {-1, 2+sqrt(3), 1}, {-1, 1+sqrt(3), 0} },
  { { 1, 0, 0}, {-1, 2+sqrt(3), 1}, {0, 1+sqrt(3), 1} },
  { { 1, 1, 1}, {-1, -1, -(2+sqrt(3))}, {-1, -1, -2} },
  { { 1, 1, 1}, {-1, -1, -(2+sqrt(3))}, {0, -1, -(1+sqrt(3))} },
  { { 1, 1, 1}, {-1, -1, -(2+sqrt(3))}, {-1, 0, -(1+sqrt(3))} },
  { { 1, 1, 0}, {-1, -1, 1}, {-1, -1, 0} },
  { { 1, 1, 0}, {-1, -1, 1}, {0, -1, 1} },
  { { 1, 1, 0}, {-1, -1, 1}, {-1, 0, 1} },
  { { 0, 0, 0}, {1, 1, 2+sqrt(3)}, {1, 0, 1+sqrt(3)} },
  { { 0, 0, 0}, {1, 1, 2+sqrt(3)}, {0, 1, 1+sqrt(3)} },
  { { 0, 0, 0}, {1, 1, 2+sqrt(3)}, {1, 1, 2} },
  { { 1, 0, 1}, {-(2+sqrt(3)), 1, -1}, {-(1+sqrt(3)), 0, -1} },
  { { 1, 0, 1}, {-(2+sqrt(3)), 1, -1}, {-2, 1, -1} },
  { { 1, 0, 1}, {-(2+sqrt(3)), 1, -1}, {-(1+sqrt(3)), 1, 0} },
  { { 0, 0, 1}, {1, 1, -1}, {1, 0, -1} },
  { { 0, 0, 1}, {1, 1, -1}, {0, 1, -1} },
  { { 0, 0, 1}, {1, 1, -1}, {1, 1, 0} },
  { { 0, 1, 1}, {1, -(2+sqrt(3)), -1}, {0, -(1+sqrt(3)), -1} },
  { { 0, 1, 1}, {1, -(2+sqrt(3)), -1}, {1, -2, -1} },
  { { 0, 1, 1}, {1, -(2+sqrt(3)), -1}, {1, -(1+sqrt(3)), 0} },
  { { 1, 0, 0}, {-1, 1, 2+sqrt(3)}, {-1, 0, 1+sqrt(3)} },
  { { 1, 0, 0}, {-1, 1, 2+sqrt(3)}, {0, 1, 1+sqrt(3)} },
  { { 1, 0, 0}, {-1, 1, 2+sqrt(3)}, {-1, 1, 2} },
  { { 1, 0, 1}, {-1, 1, -1}, {-1, 0, -1} },
  { { 1, 0, 1}, {-1, 1, -1}, {0, 1, -1} },
  { { 1, 0, 1}, {-1, 1, -1}, {-1, 1, 0} },
  { { 0, 0, 1}, {2+sqrt(3), 1, -1}, {1+sqrt(3), 0, -1} },
  { { 0, 0, 1}, {2+sqrt(3), 1, -1}, {2, 1, -1} },
  { { 0, 0, 1}, {2+sqrt(3), 1, -1}, {1+sqrt(3), 1, 0} },
  { { 1, 1, 1}, {-1, -(2+sqrt(3)), -1}, {0, -(1+sqrt(3)), -1} },
  { { 1, 1, 1}, {-1, -(2+sqrt(3)), -1}, {-1, -2, -1} },
  { { 1, 1, 1}, {-1, -(2+sqrt(3)), -1}, {-1, -(1+sqrt(3)), 0} },
  { { 1, 1, 0}, {-1, -1, 2+sqrt(3)}, {0, -1, 1+sqrt(3)} },
  { { 1, 1, 0}, {-1, -1, 2+sqrt(3)}, {-1, 0, 1+sqrt(3)} },
  { { 1, 1, 0}, {-1, -1, 2+sqrt(3)}, {-1, -1, 2} },
  { { 1, 1, 1}, {-1, -1, -1}, {0, -1, -1} },
  { { 1, 1, 1}, {-1, -1, -1}, {-1, 0, -1} },
  { { 1, 1, 1}, {-1, -1, -1}, {-1, -1, 0} },
  { { 1, 0, 1}, {-1, 2+sqrt(3), -1}, {0, 1+sqrt(3), -1} },
  { { 1, 0, 1}, {-1, 2+sqrt(3), -1}, {-1, 2, -1} },
  { { 1, 0, 1}, {-1, 2+sqrt(3), -1}, {-1, 1+sqrt(3), 0} },
  { { 0, 1, 1}, {2+sqrt(3), -1, -1}, {1+sqrt(3), 0, -1} },
  { { 0, 1, 1}, {2+sqrt(3), -1, -1}, {2, -1, -1} },
  { { 0, 1, 1}, {2+sqrt(3), -1, -1}, {1+sqrt(3), -1, 0} },
  { { 0, 1, 0}, {1, -1, 2+sqrt(3)}, {0, -1, 1+sqrt(3)} },
  { { 0, 1, 0}, {1, -1, 2+sqrt(3)}, {1, 0, 1+sqrt(3)} },
  { { 0, 1, 0}, {1, -1, 2+sqrt(3)}, {1, -1, 2} },
  { { 0, 0, 1}, {1, 2+sqrt(3), -1}, {0, 1+sqrt(3), -1} },
  { { 0, 0, 1}, {1, 2+sqrt(3), -1}, {1, 2, -1} },
  { { 0, 0, 1}, {1, 2+sqrt(3), -1}, {1, 1+sqrt(3), 0} },
  { { 0, 1, 1}, {1, -1, -1}, {0, -1, -1} },
  { { 0, 1, 1}, {1, -1, -1}, {1, 0, -1} },
  { { 0, 1, 1}, {1, -1, -1}, {1, -1, 0} },
  { { 1, 1, 1}, {-(2+sqrt(3)), -1, -1}, {-(1+sqrt(3)), 0, -1} },
  { { 1, 1, 1}, {-(2+sqrt(3)), -1, -1}, {-2, -1, -1} },
  { { 1, 1, 1}, {-(2+sqrt(3)), -1, -1}, {-(1+sqrt(3)), -1, 0} },
};

static const int normalFaces[10][4][3] = {
  {
    { 0, 3, 6 },
    { 1, 9, 4 },
    { 2, 7, 10 },
    { 8, 5, 11 },
  },
  {
    { 12, 15, 18 },
    { 13, 19, 21 },
    { 14, 22, 16 },
    { 20, 17, 23 },
  },
  {
    { 24, 27, 30 },
    { 25, 31, 33 },
    { 34, 32, 28 },
    { 26, 35, 29 },
  },
  {
    { 36, 39, 42 },
    { 45, 40, 37 },
    { 46, 38, 43 },
    { 47, 44, 41 },
  },
  {
    { 48, 51, 54 },
    { 49, 57, 52 },
    { 58, 55, 53 },
    { 50, 56, 59 },
  },
  {
    { 63, 66, 60 },
    { 64, 61, 69 },
    { 65, 70, 67 },
    { 62, 68, 71 },
  },
  {
    { 72, 75, 78 },
    { 73, 79, 81 },
    { 74, 82, 76 },
    { 80, 77, 83 },
  },
  {
    { 84, 87, 90 },
    { 85, 93, 88 },
    { 86, 91, 94 },
    { 92, 89, 95 },
  },
  {
    { 96, 99, 102 },
    { 97, 105, 100 },
    { 103, 106, 98 },
    { 104, 101, 107 },
  },
  {
    { 108, 111, 114 },
    { 109, 115, 117 },
    { 110, 118, 112 },
    { 113, 119, 116 },
  },
};

static const int bevelFaces[10][10][5] = {
  {
    { 4,  3, 0, 1, 4 },
    { 4,  0, 6, 7, 2 },
    { 4,  9, 1, 2, 10 },
    { 4,  6, 3, 5, 8 },
    { 4,  4, 9, 11, 5 },
    { 4,  10, 7, 8, 11 },
    { 3,  0, 2, 1 },
    { 3,  3, 4, 5 },
    { 3,  6, 8, 7 },
    { 3,  9, 10, 11 },
  },
  {
    { 4,  15, 12, 14, 16 },
    { 4,  12, 18, 19, 13 },
    { 4,  13, 21, 22, 14 },
    { 4,  18, 15, 17, 20 },
    { 4,  16, 22, 23, 17 },
    { 4,  21, 19, 20, 23 },
    { 3,  12, 13, 14 },
    { 3,  15, 16, 17 },
    { 3,  18, 20, 19 },
    { 3,  21, 23, 22 },
  },
  {
    { 4,  27, 24, 26, 29 },
    { 4,  24, 30, 31, 25 },
    { 4,  25, 33, 35, 26 },
    { 4,  30, 27, 28, 32 },
    { 4,  34, 28, 29, 35 },
    { 4,  33, 31, 32, 34 },
    { 3,  24, 25, 26 },
    { 3,  27, 29, 28 },
    { 3,  30, 32, 31 },
    { 3,  33, 34, 35 },
  },
  {
    { 4,  39, 36, 37, 40 },
    { 4,  36, 42, 43, 38 },
    { 4,  45, 37, 38, 46 },
    { 4,  42, 39, 41, 44 },
    { 4,  40, 45, 47, 41 },
    { 4,  46, 43, 44, 47 },
    { 3,  36, 38, 37 },
    { 3,  39, 40, 41 },
    { 3,  42, 44, 43 },
    { 3,  45, 46, 47 },
  },
  {
    { 4,  51, 48, 49, 52 },
    { 4,  48, 54, 56, 50 },
    { 4,  57, 49, 50, 59 },
    { 4,  54, 51, 53, 55 },
    { 4,  52, 57, 58, 53 },
    { 4,  55, 58, 59, 56 },
    { 3,  48, 50, 49 },
    { 3,  51, 52, 53 },
    { 3,  54, 55, 56 },
    { 3,  57, 59, 58 },
  },
  {
    { 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, 76 },
    { 4,  72, 78, 79, 73 },
    { 4,  73, 81, 82, 74 },
    { 4,  78, 75, 77, 80 },
    { 4,  76, 82, 83, 77 },
    { 4,  81, 79, 80, 83 },
    { 3,  72, 73, 74 },
    { 3,  75, 76, 77 },
    { 3,  78, 80, 79 },
    { 3,  81, 83, 82 },
  },
  {
    { 4,  87, 84, 85, 88 },
    { 4,  84, 90, 91, 86 },
    { 4,  93, 85, 86, 94 },
    { 4,  90, 87, 89, 92 },
    { 4,  88, 93, 95, 89 },
    { 4,  94, 91, 92, 95 },
    { 3,  84, 86, 85 },
    { 3,  87, 88, 89 },
    { 3,  90, 92, 91 },
    { 3,  93, 94, 95 },
  },
  {
    { 4,  99, 96, 97, 100 },
    { 4,  96, 102, 103, 98 },
    { 4,  105, 97, 98, 106 },
    { 4,  102, 99, 101, 104 },
    { 4,  100, 105, 107, 101 },
    { 4,  106, 103, 104, 107 },
    { 3,  96, 98, 97 },
    { 3,  99, 100, 101 },
    { 3,  102, 104, 103 },
    { 3,  105, 106, 107 },
  },
  {
    { 4,  111, 108, 110, 112 },
    { 4,  108, 114, 115, 109 },
    { 4,  109, 117, 118, 110 },
    { 4,  114, 111, 113, 116 },
    { 4,  112, 118, 119, 113 },
    { 4,  117, 115, 116, 119 },
    { 3,  108, 109, 110 },
    { 3,  111, 112, 113 },
    { 3,  114, 116, 115 },
    { 3,  117, 119, 118 },
  },
};