/*from Dan Barbasch and Dan Ciubotaru
all facets, some conunted more than once */

facets:=
{{-1/2,1/2,1/2,1/2,1/2,1/2,-3/2,3/2},
{-1/2,1/2,1/2,1/2,1/2,1/2,-5/2,5/2},
{-1/2,1/2,1/2,1/2,3/2,3/2,-5/2,5/2},
{-1/2,1/2,1/2,1/2,3/2,3/2,-7/2,7/2},
{-1/2,1/2,3/2,3/2,5/2,5/2,-11/2,11/2},
{-1/4,1/4,1/4,1/4,1/4,1/4,-3/4,3/4},
{-1/4,1/4,1/4,1/4,3/4,3/4,-5/4,5/4},
{-1/6,1/6,1/6,1/6,1/6,1/6,-1/2,1/2},
{-1/6,1/6,1/6,1/6,1/2,1/2,-5/6,5/6},
{-1/6,1/6,1/6,1/6,1/2,1/2,-7/6,7/6},
{-1/6,1/6,1/6,1/2,1/2,5/6,-7/6,7/6},
{-1/8,1/8,1/8,3/8,3/8,5/8,-7/8,7/8},
{-1/8,1/8,1/8,3/8,3/8,5/8,-9/8,9/8},
{0,0,0,0,0,0,-0,0},
{0,0,0,0,0,0,-1/2,1/2},
{0,0,0,0,0,0,-1,1},
{0,0,0,0,0,1,-1/2,1/2},
{0,0,0,0,0,1,-3/2,3/2},
{0,0,0,0,1/2,1/2,-1/2,1/2},
{0,0,0,0,1/2,1/2,-1,1},
{0,0,0,0,1/2,1/2,-3/2,3/2},
{0,0,0,0,1,1,-1,1},
{0,0,0,0,1,1,-2,2},
{0,0,0,0,1,2,-5/2,5/2},
{0,0,0,1/3,1/3,1/3,-1/2,1/2},
{0,0,0,1/2,1/2,1/2,-3/4,3/4},
{0,0,0,1/2,1/2,1/2,-5/4,5/4},
{0,0,0,1/2,1/2,1,-3/2,3/2},
{0,0,0,1,1,1,-3/2,3/2},
{0,0,0,1,1,1,-5/2,5/2},
{0,0,1/4,1/4,1/4,1/4,-1/2,1/2},
{0,0,1/4,1/4,1/2,1/2,-3/4,3/4},
{0,0,1/4,1/4,1/2,1/2,-5/4,5/4},
{0,0,1/4,1/2,1/2,3/4,-5/4,5/4},
{0,0,1/3,1/3,1/3,1/3,-2/3,2/3},
{0,0,1/3,1/3,1/3,2/3,-5/6,5/6},
{0,0,1/3,1/3,1/3,2/3,-7/6,7/6},
{0,0,1/3,1/3,2/3,2/3,-4/3,4/3},
{0,0,1/3,1/3,2/3,1,-3/2,3/2},
{0,0,1/2,1/2,1/2,1/2,-1,1},
{0,0,1/2,1/2,1/2,1/2,-3/2,3/2},
{0,0,1/2,1/2,1/2,1,-5/4,5/4},
{0,0,1/2,1/2,1,1,-3/2,3/2},
{0,0,1/2,1/2,1,1,-2,2},
{0,0,1/2,1/2,1,1,-5/2,5/2},
{0,0,1/2,1/2,1,3/2,-9/4,9/4},
{0,0,1/2,1/2,1,2,-5/2,5/2},
{0,0,1/2,1/2,3/2,3/2,-5/2,5/2},
{0,0,1,1,1,1,-2,2},
{0,0,1,1,1,2,-5/2,5/2},
{0,0,1,1,1,2,-7/2,7/2},
{0,0,1,1,2,2,-3,3},
{0,0,1,1,2,2,-4,4},
{0,0,1,1,2,3,-9/2,9/2},
{0,1/4,1/4,1/4,3/4,1,-3/2,3/2},
{0,1/4,1/4,1/2,1/2,1,-5/4,5/4},
{0,1/4,1/2,1/2,3/4,1,-7/4,7/4},
{0,1/3,1/3,1/3,2/3,1,-4/3,4/3},
{0,1/3,1/3,2/3,2/3,1,-11/6,11/6},
{0,1/3,1/3,2/3,1,4/3,-13/6,13/6},
{0,1/3,1/3,2/3,1,5/3,-7/3,7/3},
{0,1/3,1/3,2/3,1,2,-5/2,5/2},
{0,1/2,1/2,1/2,1/2,1,-3/2,3/2},
{0,1/2,1/2,1/2,1/2,1,-5/2,5/2},
{0,1/2,1/2,1/2,1,3/2,-5/2,5/2},
{0,1/2,1/2,1,1,2,-5/2,5/2},
{0,1/2,1/2,1,1,2,-7/2,7/2},
{0,1/2,1/2,1,3/2,3/2,-7/2,7/2},
{0,1/2,1/2,1,3/2,2,-13/4,13/4},
{0,1/2,1/2,1,2,3,-9/2,9/2},
{0,1,1,2,2,3,-11/2,11/2},
{0,1,1,2,3,4,-13/2,13/2},
{0,1,2,3,4,5,-17/2,17/2},
{1/8,1/8,1/8,3/8,3/8,3/8,-5/8,5/8},
{1/8,1/8,3/8,3/8,5/8,7/8,-11/8,11/8},
{1/6,1/6,1/6,1/6,1/2,1/2,-2/3,2/3},
{1/6,1/6,1/6,1/2,1/2,1/2,-3/2,3/2},
{1/6,1/6,1/6,1/2,1/2,5/6,-4/3,4/3},
{1/6,1/6,1/2,1/2,1/2,5/6,-3/2,3/2},
{1/4,1/4,1/4,1/4,1/4,1/4,-1/2,1/2},
{1/4,1/4,1/4,1/4,1/4,3/4,-3/4,3/4},
{1/4,1/4,1/4,1/4,1/4,3/4,-5/4,5/4},
{1/4,1/4,1/4,1/4,3/4,3/4,-3/2,3/2},
{1/4,1/4,1/4,1/2,1/2,3/4,-3/2,3/2},
{1/4,1/4,1/4,3/4,5/4,7/4,-5/2,5/2},
{1/2,1/2,1/2,1/2,1/2,1/2,-1,1},
{-1/4,1/4,1/4,1/2,1/2,1/2,-11/8,11/8},
{-1/4,1/4,1/4,3/4,3/4,3/4,-3/2,3/2},
{-1/4,1/4,3/8,3/8,1/2,1/2,-11/8,11/8},
{-1/4,1/4,5/12,5/12,7/12,7/12,-17/12,17/12},
{-1/4,1/4,5/12,5/12,7/12,3/4,-3/2,3/2},
{-1/4,1/4,1/2,1/2,3/4,3/4,-3/2,3/2},
{-3/16,5/16,7/16,7/16,9/16,11/16,-23/16,23/16},
{-1/8,3/8,3/8,3/8,5/8,5/8,-3/2,3/2},
{-1/8,3/8,3/8,1/2,1/2,5/8,-3/2,3/2},
{-1/4,1/4,1/4,3/4,3/4,3/4,-5/2,5/2},
{-1/4,1/4,1/2,1/2,3/4,3/4,-5/2,5/2},
{-1/8,3/8,3/8,5/8,11/8,13/8,-5/2,5/2},
{-1/4,1/4,3/4,3/4,5/4,7/4,-7/2,7/2},
{-1/4,1/2,1/2,3/4,5/4,7/4,-7/2,7/2},
{-5/24,5/24,5/24,5/24,5/24,5/24,-5/8,5/8},
{-1/8,1/8,1/8,1/8,3/8,3/8,-5/8,5/8},
{-1/8,1/8,1/8,7/24,7/24,7/24,-5/8,5/8},
{-1/8,1/8,1/8,3/8,3/8,3/8,-3/4,3/4},
{-1/8,1/8,1/4,1/4,1/4,1/4,-5/8,5/8},
{-1/8,1/8,1/4,1/4,3/8,3/8,-3/4,3/4},
{-1/8,1/8,7/24,7/24,7/24,7/24,-17/24,17/24},
{-1/16,3/16,3/16,5/16,5/16,5/16,-11/16,11/16},
{-5/24,5/24,5/24,3/8,5/8,19/24,-29/24,29/24},
{-1/12,1/12,1/12,1/12,1/12,1/12,-1/4,1/4},
{-1/12,1/12,1/12,1/4,1/4,1/4,-1/2,1/2},
{-7/48,7/48,7/48,13/48,7/16,9/16,-41/48,41/48},
{-1/12,1/12,1/12,1/3,1/2,1/2,-19/24,19/24},
{-1/12,1/12,5/24,5/24,1/2,1/2,-19/24,19/24},
{-1/12,1/12,1/3,1/3,1/2,1/2,-11/12,11/12},
{-7/48,7/48,7/48,13/48,7/16,9/16,-55/48,55/48},
{-1/12,1/12,1/12,1/3,1/2,1/2,-29/24,29/24},
{-1/12,1/12,1/4,1/4,5/12,7/12,-7/6,7/6},
{-1/12,1/12,1/3,1/3,1/2,1/2,-13/12,13/12},
{-1/12,1/12,5/24,1/2,1/2,19/24,-29/24,29/24},
{-1/16,1/16,1/16,7/16,7/16,9/16,-13/16,13/16},
{-1/16,1/16,5/16,7/16,7/16,9/16,-15/16,15/16},
{-1/16,1/16,1/16,3/16,11/16,13/16,-17/16,17/16},
{-1/12,1/12,1/12,1/12,1/12,1/12,-1/2,1/2},
{0,0,0,0,0,0,-1/4,1/4},
{0,0,0,0,1/4,1/4,-1/2,1/2},
{0,0,1/8,1/8,1/8,1/8,-1/2,1/2},
{1/8,1/8,1/8,1/8,1/8,1/8,-1/2,1/2},
{-1/8,1/8,1/8,1/8,1/8,1/8,-7/8,7/8},
{-1/12,1/12,1/12,1/12,1/12,1/12,-3/4,3/4},
{-1/12,1/12,1/12,1/12,1/4,1/4,-11/12,11/12},
{-1/16,1/16,1/16,3/16,3/16,5/16,-15/16,15/16},
{0,0,0,0,1/4,1/4,-3/4,3/4},
{0,0,0,0,1/4,1/4,-1,1},
{0,0,0,1/6,1/6,1/6,-3/4,3/4},
{0,0,0,1/4,1/4,1/4,-7/8,7/8},
{0,0,1/8,1/8,1/8,1/8,-3/4,3/4},
{0,0,1/8,1/8,1/4,1/4,-7/8,7/8},
{0,0,1/6,1/6,1/6,1/6,-5/6,5/6},
{0,0,1/6,1/6,1/6,1/3,-11/12,11/12},
{0,0,1/4,1/4,1/4,1/4,-1,1},
{1/16,1/16,1/16,3/16,3/16,3/16,-13/16,13/16},
{1/12,1/12,1/12,1/12,1/4,1/4,-5/6,5/6},
{1/8,1/8,1/8,1/8,1/8,1/8,-3/4,3/4},
{1/8,1/8,1/8,1/8,1/8,3/8,-7/8,7/8},
{1/4,1/4,1/4,1/4,1/4,1/4,-1,1},
{-1/8,1/8,1/8,1/8,1/8,5/8,-5/8,5/8},
{-1/12,1/12,1/12,1/12,1/12,7/12,-1/2,1/2},
{-1/12,1/12,1/12,1/12,1/4,3/4,-2/3,2/3},
{-1/16,1/16,1/16,3/16,3/16,13/16,-11/16,11/16},
{0,0,0,0,0,1/2,-1/4,1/4},
{0,0,0,0,0,1/2,-1/2,1/2},
{0,0,0,0,0,1/2,-3/4,3/4},
{0,0,0,0,1/4,3/4,-1/2,1/2},
{0,0,0,0,1/4,3/4,-3/4,3/4},
{0,0,0,1/6,1/6,2/3,-1/2,1/2},
{0,0,0,1/4,1/4,3/4,-5/8,5/8},
{0,0,1/8,1/8,1/8,5/8,-1/2,1/2},
{0,0,1/8,1/8,1/4,3/4,-5/8,5/8},
{0,0,1/6,1/6,1/6,2/3,-7/12,7/12},
{0,0,1/6,1/6,1/6,5/6,-2/3,2/3},
{1/16,1/16,1/16,3/16,3/16,11/16,-9/16,9/16},
{1/12,1/12,1/12,1/12,1/4,3/4,-7/12,7/12},
{1/8,1/8,1/8,1/8,1/8,5/8,-1/2,1/2},
{1/8,1/8,1/8,1/8,1/8,7/8,-5/8,5/8},
{-1/4,1/4,1/4,1/4,1/4,3/4,-3/2,3/2},
{0,0,0,0,1/4,3/4,-3/2,3/2},
{0,0,0,0,1/2,1,-5/4,5/4},
{0,0,0,1/4,1/4,1,-3/2,3/2},
{0,0,1/6,1/6,1/3,1,-3/2,3/2},
{0,0,1/4,1/4,1/4,3/4,-3/2,3/2},
{0,0,1/4,1/4,1/4,1,-11/8,11/8},
{0,1/8,1/8,1/8,3/8,1,-3/2,3/2},
{0,1/8,1/8,1/4,1/4,1,-11/8,11/8},
{0,1/6,1/6,1/6,1/3,1,-17/12,17/12},
{0,1/4,1/4,1/4,1/4,1,-3/2,3/2},
{1/12,1/12,1/12,1/4,1/4,3/4,-3/2,3/2},
{1/8,1/8,1/8,1/8,3/8,7/8,-3/2,3/2},
{-1/12,1/12,1/12,1/12,1/3,1/3,-1/2,1/2},
{0,0,0,0,1/4,1/4,-1/4,1/4},
{0,0,0,1/6,5/12,5/12,-1/2,1/2},
{0,0,1/8,1/8,3/8,3/8,-1/2,1/2},
{0,0,1/6,1/6,5/12,5/12,-7/12,7/12},
{1/16,1/16,1/16,3/16,7/16,7/16,-9/16,9/16},
{-1/12,1/12,1/12,1/12,1/2,1/2,-11/12,11/12},
{-1/16,1/16,1/16,3/16,7/16,9/16,-15/16,15/16},
{0,0,0,1/4,1/2,1/2,-7/8,7/8},
{0,0,1/8,1/8,1/2,1/2,-7/8,7/8},
{0,0,1/4,1/4,1/2,1/2,-1,1},
{1/12,1/12,1/12,1/12,1/2,1/2,-5/6,5/6},
{1/4,1/4,1/4,1/4,1/2,1/2,-1,1},
{-1/4,1/4,1/4,1/4,1/2,1/2,-3/2,3/2},
{0,0,1/4,1/4,1/2,1/2,-3/2,3/2},
{1/12,1/12,1/12,1/4,1/2,1/2,-3/2,3/2},
{-1/8,1/8,1/8,1/8,7/8,7/8,-9/8,9/8},
{-1/12,1/12,1/12,1/4,3/4,11/12,-13/12,13/12},
{0,0,1/4,1/4,3/4,3/4,-1,1},
{0,0,1/4,1/4,3/4,1,-9/8,9/8},
{0,1/8,1/8,1/4,3/4,1,-9/8,9/8},
{1/12,1/12,1/12,1/4,3/4,11/12,-7/6,7/6},
{1/8,1/8,1/8,1/8,5/8,7/8,-9/8,9/8},
{1/4,1/4,1/4,1/4,3/4,3/4,-1,1},
{0,0,1/4,1/4,1,1,-2,2},
{0,0,1/4,1/4,1,2,-5/2,5/2},
{0,1/6,1/6,1/3,1,2,-5/2,5/2},
{0,0,0,1/6,1/6,1/6,-1/4,1/4},
{0,0,0,1/6,1/6,1/6,-1/2,1/2},
{0,0,1/8,7/24,7/24,7/24,-1/2,1/2},
{0,0,1/6,1/3,1/3,1/3,-7/12,7/12},
{0,0,1/8,3/8,1/2,1/2,-3/4,3/4},
{0,0,1/6,5/12,5/12,5/12,-17/24,17/24},
{0,0,1/6,5/12,5/12,7/12,-19/24,19/24},
{0,0,1/4,1/2,1/2,1/2,-7/8,7/8},
{-1/8,1/8,1/8,3/8,5/8,5/8,-5/4,5/4},
{0,0,1/8,3/8,1/2,1/2,-5/4,5/4},
{0,0,1/8,1/2,1/2,5/8,-5/4,5/4},
{0,0,1/6,5/12,5/12,7/12,-29/24,29/24},
{0,0,1/6,5/12,7/12,7/12,-31/24,31/24},
{1/4,1/4,1/4,1/2,1/2,1/2,-9/8,9/8},
{-1/4,1/4,1/4,1/2,1/2,3/4,-3/2,3/2},
{0,0,1/6,5/12,7/12,1,-3/2,3/2},
{0,0,1/4,1/2,1/2,3/4,-3/2,3/2},
{0,0,1/4,1/2,1/2,1,-11/8,11/8},
{0,1/6,1/6,5/12,7/12,1,-17/12,17/12},
{0,1/4,1/4,1/2,1/2,1,-3/2,3/2},
{0,0,1/6,2/3,5/6,1,-3/2,3/2},
{0,0,1/4,3/4,1,1,-3/2,3/2},
{1/16,1/16,3/16,11/16,13/16,15/16,-23/16,23/16},
{0,0,1/4,3/4,1,1,-5/2,5/2},
{0,1/4,1/4,3/4,1,5/4,-5/2,5/2},
{-1/12,1/12,5/24,5/24,5/24,5/24,-1/2,1/2},
{0,0,1/8,1/8,1/8,1/8,-1/4,1/4},
{0,0,7/24,7/24,5/12,5/12,-17/24,17/24},
{-1/12,1/12,5/24,5/24,1/2,1/2,-29/24,29/24},
{-1/8,1/8,1/4,3/8,5/8,3/4,-5/4,5/4},
{0,0,1/8,1/4,3/4,7/8,-9/8,9/8},
{1/12,1/12,5/24,1/2,1/2,19/24,-31/24,31/24},
{1/12,1/12,1/4,1/4,5/12,5/12,-2/3,2/3},
{-1/12,1/12,1/4,1/4,5/12,7/12,-5/6,5/6},
{-1/16,1/16,11/48,17/48,17/48,31/48,-41/48,41/48},
{0,0,1/6,1/6,5/12,7/12,-11/12,11/12},
{0,0,5/12,5/12,5/12,7/12,-11/12,11/12},
{-1/8,1/8,7/24,7/24,13/24,17/24,-29/24,29/24},
{-1/12,1/12,1/4,5/12,5/12,3/4,-7/6,7/6},
{-1/16,1/16,11/48,17/48,17/48,31/48,-55/48,55/48},
{0,0,1/6,1/6,2/3,5/6,-13/12,13/12},
{-1/8,1/8,7/24,7/24,17/24,17/24,-31/24,31/24},
{0,0,1/6,1/6,5/6,5/6,-7/6,7/6},
{1/12,1/12,1/4,5/12,7/12,3/4,-4/3,4/3},
{0,0,5/12,5/12,5/6,1,-3/2,3/2},
{1/8,1/8,7/24,7/24,17/24,7/8,-3/2,3/2},
{-1/16,1/16,5/16,7/16,7/16,9/16,-17/16,17/16},
{-1/4,1/4,1/2,1/2,1/2,1/2,-3/2,3/2},
{0,0,5/12,5/12,7/12,7/12,-17/12,17/12},
{1/12,1/12,1/3,1/2,1/2,2/3,-17/12,17/12},
{1/8,1/8,3/8,1/2,1/2,5/8,-3/2,3/2},
{-1/8,1/8,3/8,3/8,5/8,7/8,-5/4,5/4},
{-1/12,1/12,1/3,1/2,1/2,11/12,-29/24,29/24},
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