/*from Dan Barbasch and Dan Ciubotar */

facets:={
{11/2,5/2,3/2,1/2},
{7/2,3/2,1/2,1/2},
{5/2,3/2,1/2,1/2},
{3/2,1/2,1/2,1/2},
{5/2,1/2,1/2,1/2},
{5/2,5/4,1/2,1/4},
{5/2,3/4,1/2,1/4},
{5/2,1,1/2,0},
{5/2,3/2,1/2,0},
{5/2,3/2,1/2,1/4},
{3/2,1/2,1/2,0},
{3/2,1/2,1/2,1/4},
{1,1/2,1/2,0},
{7/6,1/2,1/6,1/6},
{5/4,1/2,1/4,0},
{11/8,4/8,3/8,2/8},
{29/24,12/24,5/24,2/24},
{13/12,6/12,4/12,1/12},
{5/4,3/4,1/4,1/4},
{4/3,2/3,1/3,0},
{31/24,17/24,7/24,3/24},
{17/12,7/12,5/12,3/12},
{3/2,1/2,0,0},
{3/2,1/2,1/4,1/8},
{3/2,1/2,1/4,1/4},
{1,0,0,0},
{1,1/4,1/4,0},
{1,1,0,0},
{5/4,3/4,1/4,1/12},
{17/12,7/12,5/12,1/12},
{9/8,1/2,1/8,1/8},
{1,1/2,0,0},
{1,1/2,1/4,0},
{7/8,4/8,2/8,1/8},
{5/6,3/6,1/6,1/6},
{7/8,4/8,1/8,1/8},
{13/16,8/16,3/16,2/16},
{3/4,1/2,1/4,0},
{7/8,2/8,1/8,0},
{7/8,3/8,1/8,1/8},
{13/16,5/16,3/16,1/16},
{11/8,4/8,3/8,1/8},
{9/8,4/8,1/8,1/16},
{17/16,8/16,3/16,1/16},
{15/16,8/16,4/16,1/16},
{15/16,7/16,5/16,1/16},
{10/12,6/12,2/12,1/12},
{10/12,5/12,2/12,1/12},
{3/4,1/4,1/4,1/4},
{1/2,1/2,0,0},
{11/16,5/16,1/16,1/16},
{1/2,0,0,0},
{1/2,1/6,1/6,1/6},
{1/2,1/4,1/4,0},
{4/6,1/6,1/6,0},
{1/2,1/4,1/8,1/16},
{27/48,13/48,5/48,3/48},
{27/48,13/48,9/48,1/48},
{0,0,0,0},
{1/4,1/8,1/16,1/32},
{4/6,1/6,1/6,1/6},
{5/8,3/8,0,0}{1/4,0,0,3/8},
{9/8,7/8,1/8,1/8}
};