B3

# point representatives from each cell, grouped by Weyl face

face   {1, 2, 3}
                                       0

face   {2, 3}
[1, 0, 0]   {}   {1}   {}
                                       q

face   {1, 3}
[0, 1, 0]   {}   {2}   {4}
                                       q

face   {3}
[5/4, 1, 0]   {}   {2}   {1}
[1, 1, 0]   {}   {1, 2}   {5}
[1/4, 1, 0]   {1}   {2}   {5}
[0, 1/2, 0]   {5}   {4}   {}
[1/4, 3/4, 0]   {1, 2}   {5}   {4}
                                           2
                                    4 q + q

face   {1, 2}
[0, 0, 1]   {}   {3}   {7}
                                       q

face   {2}
[1, 0, 5/4]   {}   {1}   {3}
[5/4, 0, 1]   {}   {3}   {1}
[1, 0, 1]   {}   {1, 3}   {8}
[1/4, 0, 1]   {1}   {3}   {8}
[1, 0, 1/4]   {3}   {1}   {8}
[1/4, 0, 3/4]   {1, 3}   {8}   {7}
                                           2
                                    5 q + q

face   {1}
[0, 1, 5/4]   {}   {2}   {3, 4}
[0, 1, 1]   {}   {2, 3}   {4, 6}
[0, 1, 1/4]   {3}   {2}   {4, 6}
[0, 3/4, 1/4]   {2, 3}   {6}   {4}
[0, 1/2, 1/2]   {2, 3}   {4, 6}   {9}
[0, 3/8, 5/8]   {3, 4}   {6}   {9}
                                            2
                                   4 q + 2 q

face   {}
[5/4, 5/4, 5/4]   {}   {}   {1, 2, 3}
[1, 5/4, 5/4]   {}   {1}   {2, 3}
[0, 5/4, 5/4]   {1}   {}   {2, 3}
[5/4, 1, 5/4]   {}   {2}   {1, 3}
[5/4, 0, 5/4]   {2}   {}   {1, 3}
[1, 1, 5/4]   {}   {1, 2}   {3, 5}
[1/4, 1, 5/4]   {1}   {2}   {3, 5}
[1, 1/4, 5/4]   {2}   {1}   {3, 5}
[1/2, 3/4, 5/4]   {1, 2}   {}   {3, 5}
[5/4, 5/4, 1]   {}   {3}   {1, 2}
[5/4, 5/4, 0]   {3}   {}   {1, 2}
[1, 5/4, 1]   {}   {1, 3}   {2}
[0, 5/4, 1]   {1}   {3}   {2}
[1, 5/4, 0]   {3}   {1}   {2}
[0, 5/4, 0]   {1, 3}   {}   {2}
[5/4, 1, 1]   {}   {2, 3}   {1, 6}
[5/4, 1/4, 1]   {2}   {3}   {1, 6}
[5/4, 1, 1/4]   {3}   {2}   {1, 6}
[5/4, 3/4, 1/2]   {2, 3}   {}   {1, 6}
[1, 1, 1]   {}   {1, 2, 3}   {5, 6}
[1/4, 1, 1]   {1}   {2, 3}   {5, 6}
[1, 1/4, 1]   {2}   {1, 3}   {5, 6}
[1/2, 3/4, 1]   {1, 2}   {3}   {5, 6}
[1, 1, 1/4]   {3}   {1, 2}   {5, 6}
[1/4, 1, 1/4]   {1, 3}   {2}   {5, 6}
[1, 3/4, 1/2]   {2, 3}   {1}   {5, 6}
[1/2, 3/4, 1/2]   {1, 2, 3}   {}   {5, 6}
[0, 1/2, 5/4]   {5}   {4}   {3}
[0, 0, 5/4]   {4}   {}   {3}
[0, 1/2, 1]   {5}   {3, 4}   {6}
[0, 1/2, 3/4]   {3, 5}   {4}   {6}
[0, 1/4, 1]   {4}   {3}   {6}
[0, 7/16, 11/16]   {3, 4}   {}   {6}
[1/4, 3/8, 5/8]   {3, 5}   {4, 6}   {8}
[1/4, 1/4, 3/4]   {3, 4}   {6}   {8}
[1/2, 1/4, 1/2]   {5, 6}   {4}   {8}
[1/2, 0, 3/4]   {4, 6}   {}   {8}
[1/4, 3/4, 5/4]   {1, 2}   {5}   {3, 4}
[0, 5/8, 5/4]   {5}   {}   {3, 4}
[1/4, 3/4, 1]   {1, 2}   {3, 5}   {4, 6}
[1/4, 3/4, 1/2]   {1, 2, 3}   {5}   {4, 6}
[0, 5/8, 1]   {5}   {3}   {4, 6}
[0, 3/4, 1/2]   {3, 5}   {}   {4, 6}
[5/4, 3/4, 1/4]   {2, 3}   {6}   {1}
[5/4, 0, 0]   {6}   {}   {1}
[1, 3/4, 1/4]   {2, 3}   {1, 6}   {5}
[1/2, 3/4, 1/4]   {1, 2, 3}   {6}   {5}
[1, 1/4, 0]   {6}   {1}   {5}
[1/2, 3/4, 0]   {1, 6}   {}   {5}
[1/4, 3/4, 1/4]   {1, 2, 3}   {5, 6}   {4, 8}
[1/4, 1/2, 1/2]   {3, 5}   {6}   {4, 8}
[1/2, 1/2, 1/4]   {1, 6}   {5}   {4, 8}
[1/4, 7/16, 7/16]   {5, 6}   {}   {4, 8}
[0, 0, 1/2]   {9}   {7}   {}
[0, 0, 0]   {7}   {}   {}
[1/4, 1/2, 1/4]   {5, 6}   {8}   {4}
[0, 5/8, 0]   {8}   {}   {4}
[1/4, 3/8, 3/8]   {5, 6}   {4, 8}   {9}
[1/4, 1/4, 1/2]   {4, 6}   {8}   {9}
[0, 1/2, 1/4]   {8}   {4}   {9}
[0, 1/4, 5/8]   {4, 8}   {}   {9}
[0, 1/4, 1/2]   {4, 8}   {9}   {7}
[0, 0, 5/8]   {9}   {}   {7}
                                             2    3
                             20 + 30 q + 12 q  + q