A4

# point representatives from each cell, grouped by Weyl face

face   {1, 2}
                                       0

face   {2}
[1, 0, 0, 1]   {}   {1}   {10}
                                       q

face   {1}
[0, 1, 1, 0]   {}   {2}   {6}
[0, 1/2, 1/2, 0]   {2}   {6}   {}
                                      2 q

face   {}
[5/4, 5/4, 5/4, 5/4]   {}   {}   {1, 2}
[1, 5/4, 5/4, 1]   {}   {1}   {2}
[0, 5/4, 5/4, 0]   {1}   {}   {2}
[5/4, 1, 1, 5/4]   {}   {2}   {1, 6}
[5/4, 5/8, 5/8, 5/4]   {2}   {}   {1, 6}
[1, 1, 1, 1]   {}   {1, 2}   {5, 6}
[1/4, 1, 1, 1/4]   {1}   {2}   {5, 6}
[1, 5/8, 5/8, 1]   {2}   {1}   {5, 6}
[1/2, 3/4, 3/4, 1/2]   {1, 2}   {}   {5, 6}
[1/4, 3/4, 3/4, 1/4]   {1, 2}   {5}   {6}
[0, 5/8, 5/8, 0]   {5}   {}   {6}
[5/4, 1/2, 1/2, 5/4]   {2}   {6}   {1}
[5/4, 0, 0, 5/4]   {6}   {}   {1}
[1, 1/2, 1/2, 1]   {2}   {1, 6}   {5}
[3/4, 1/2, 1/2, 3/4]   {1, 2}   {6}   {5}
[1, 1/4, 1/4, 1]   {6}   {1}   {5}
[11/16, 7/16, 7/16, 11/16]   {1, 6}   {}   {5}
[1/2, 1/2, 1/2, 1/2]   {1, 2}   {5, 6}   {8}
[1/4, 1/2, 1/2, 1/4]   {5}   {6}   {8}
[5/8, 3/8, 3/8, 5/8]   {1, 6}   {5}   {8}
[1/4, 7/16, 7/16, 1/4]   {5, 6}   {}   {8}
[1/4, 3/8, 3/8, 1/4]   {5, 6}   {8}   {10}
[1/2, 1/8, 1/8, 1/2]   {8}   {}   {10}
[1/4, 1/4, 1/4, 1/4]   {8}   {10}   {}
[0, 0, 0, 0]   {10}   {}   {}
                                               2
                                10 + 12 q + 3 q