/*from Dan Barbasch and Dan Ciubotaru */ facets:= {{0,1,2,3,4,-4,-4,4}, {0,1,1,2,3,-3,-3,3}, {0,0,1,1,2,-2,-2,2}, {1/2,1/2,3/2,3/2,5/2,-5/2,-5/2,5/2}, {1/4,3/4,3/4,5/4,7/4,-7/4,-7/4,7/4}, {0,1/4,3/4,1,2,-2,-2,2}, {0,1/2,1/2,1,3/2,-3/2,-3/2,3/2}, {3/8,5/8,9/8,11/8,13/8,-13/8,-13/8,13/8}, {1/2,1/2,3/2,3/2,3/2,-3/2,-3/2,3/2}, {1/4,1/2,1/2,3/4,3/2,-3/2,-3/2,3/2}, {1/2,1/2,1/2,1/2,3/2,-3/2,-3/2,3/2}, {0,0,1,1,1,-1,-1,1}, {0,1/4,3/4,1,1,-1,-1,1}, {0,0,1/2,1/2,1,-1,-1,1}, {0,1/6,5/12,7/12,1,-1,-1,1}, {0,1/3,1/3,2/3,1,-1,-1,1}, {0,1/6,2/3,5/6,1,-1,-1,1}, {1/2,1/2,1/2,1/2,1,-1,-1,1}, {1/4,1/4,3/4,3/4,1,-1,-1,1}, {1/8,3/8,5/8,7/8,1,-1,-1,1}, {-1/4,1/4,1/4,3/4,3/4,-3/4,-3/4,3/4}, {-1/24,5/24,3/8,5/8,19/24,-19/24,-19/24,19/24}, {1/6,1/6,1/2,1/2,5/6,-5/6,-5/6,5/6}, {7/48,13/48,7/16,9/16,41/48,-41/48,-41/48,41/48}, {1/8,3/8,3/8,5/8,7/8,-7/8,-7/8,7/8}, {1/16,3/16,11/16,13/16,15/16,-15/16,-15/16,15/16}, {0,0,0,0,1,-1,-1,1}, {0,0,1/4,1/4,1,-1,-1,1}, {0,1/6,1/3,1/2,1,-1,-1,1}, {0,1/3,1/2,5/6,1,-1,-1,1}, {0,1/4,1/4,1/2,3/4,-3/4,-3/4,3/4}, {1/4,1/4,1/4,1/4,3/4,-3/4,-3/4,3/4}, {1/2,1/2,1/2,1/2,1/2,-1/2,-1/2,1/2}, {3/8,3/8,3/8,3/8,5/8,-5/8,-5/8,5/8}, {1/4,3/8,3/8,1/2,5/8,-5/8,-5/8,5/8}, {1/8,3/8,3/8,5/8,5/8,-5/8,-5/8,5/8}, {1/16,3/16,5/16,7/16,9/16,-9/16,-9/16,9/16}, {1/8,1/8,1/2,1/2,1/2,-1/2,-1/2,1/2}, {1/32,7/32,7/32,13/32,19/32,-19/32,-19/32,19/32}, {-1/8,1/8,1/8,3/8,5/8,-5/8,-5/8,5/8}, {-1/32,1/32,9/32,11/32,21/32,-21/32,-21/32,21/32}, {1/16,1/16,5/16,5/16,11/16,-11/16,-11/16,11/16}, {0,0,1/3,1/3,2/3,-2/3,-2/3,2/3}, {0,1/8,1/4,3/8,5/8,-5/8,-5/8,5/8}, {1/16,1/8,1/4,5/16,11/16,-11/16,-11/16,11/16}, {0,1/16,5/16,3/8,11/16,-11/16,-11/16,11/16}, {-1/16,3/16,5/16,9/16,11/16,-11/16,-11/16,11/16}, {-5/32,5/32,9/32,19/32,23/32,-23/32,-23/32,23/32}, {1/8,1/8,3/8,3/8,5/8,-5/8,-5/8,5/8}, {0,0,0,0,1/2,-1/2,-1/2,1/2}, {1/4,1/4,1/4,1/4,1/2,-1/2,-1/2,1/2}, {1/8,1/8,3/8,3/8,1/2,-1/2,-1/2,1/2}, {1/16,3/16,5/16,7/16,1/2,-1/2,-1/2,1/2}, {0,1/4,1/4,1/2,1/2,-1/2,-1/2,1/2}, {-1/48,3/16,13/48,23/48,25/48,-25/48,-25/48,25/48}, {7/48,13/48,13/48,19/48,29/48,-29/48,-29/48,29/48}, {3/16,3/16,3/8,3/8,5/8,-5/8,-5/8,5/8}, {13/64,15/64,23/64,25/64,41/64,-41/64,-41/64,41/64}, {0,1/16,3/16,1/4,3/8,-3/8,-3/8,3/8}, {1/24,1/12,5/24,1/4,5/12,-5/12,-5/12,5/12}, {-1/24,1/8,1/6,1/3,5/12,-5/12,-5/12,5/12}, {0,0,1/3,1/3,1/3,-1/3,-1/3,1/3}, {-1/8,1/8,1/8,3/8,3/8,-3/8,-3/8,3/8}, {1/12,1/4,1/4,5/12,5/12,-5/12,-5/12,5/12}, {0,0,0,0,0,0,0,0}, {0,0,1/4,1/4,5/12,-5/12,-5/12,5/12}};