D4

# point representatives from the cells that are psd in the
# W-representations carried by petite 0-weight spaces

face   {1, 2, 3, 4}

                                [0, 0, 0, 0, 0]

face   {2, 3, 4}

[1, 0, 0, 0]   {}   {1}   {}
                                [0, 0, 0, 0, 1]

face   {1, 3, 4}

[0, 1, 0, 0]   {}   {2}   {}
                                [0, 0, 0, 0, 1]

face   {3, 4}

[1/4, 3/4, 0, 0]   {1, 2}   {8}   {}
                                [0, 0, 0, 1, 0]

face   {1, 2, 4}

[0, 0, 1, 0]   {}   {3}   {12}
                                [0, 0, 0, 0, 1]

face   {2, 4}

[1, 0, 1, 0]   {}   {1, 3}   {5}
[1/4, 0, 3/4, 0]   {1, 3}   {5}   {12}
                                [0, 0, 0, 1, 1]

face   {1, 4}

[0, 1, 1, 0]   {}   {2, 3}   {6}
[0, 1/4, 3/4, 0]   {2, 3}   {6}   {12}
                                [0, 0, 0, 1, 1]

face   {4}

[1/4, 1/4, 1/2, 0]   {5, 6}   {8}   {12}
                                [0, 0, 1, 0, 0]

face   {1, 2, 3}

[0, 0, 0, 1]   {}   {4}   {}
                                [0, 0, 0, 0, 1]

face   {2, 3}

[1/4, 0, 0, 3/4]   {1, 4}   {9}   {}
                                [0, 0, 0, 1, 0]

face   {1, 3}

[0, 1/4, 0, 3/4]   {2, 4}   {10}   {}
                                [0, 0, 0, 1, 0]

face   {3}

[1, 1, 0, 1]   {}   {1, 2, 4}   {8, 9, 10}
[1/4, 1/4, 0, 1/2]   {8, 9, 10}   {11}   {}
                                [0, 0, 1, 0, 1]

face   {1, 2}

[0, 0, 1, 1]   {}   {3, 4}   {7}
[0, 0, 1/4, 3/4]   {3, 4}   {7}   {12}
                                [0, 0, 0, 1, 1]

face   {2}

[1/4, 0, 1/4, 1/2]   {5, 7}   {9}   {12}
                                [0, 0, 1, 0, 0]

face   {1}

[0, 1/4, 1/4, 1/2]   {6, 7}   {10}   {12}
                                [0, 0, 1, 0, 0]

face   {}

[1, 1, 1, 1]   {}   {1, 2, 3, 4}   {5, 6, 7}
[1/4, 1/4, 3/4, 1]   {1, 2, 3}   {4, 5, 6}   {7, 8}
[1/4, 1, 3/4, 1/4]   {1, 3, 4}   {2, 5, 7}   {6, 9}
[1, 3/4, 1/4, 3/4]   {2, 3, 4}   {1, 6, 7}   {5, 10}
[1/4, 1/4, 3/4, 1/4]   {1, 2, 3, 4}   {5, 6, 7}   {8, 9, 10}
[1/4, 1/4, 1/2, 1/4]   {5, 6, 7}   {8, 9, 10}   {11}
[1/4, 1/4, 0, 3/4]   {7, 8}   {9, 10}   {11}
[1/4, 3/4, 0, 1/4]   {6, 9}   {8, 10}   {11}
[1/4, 1/2, 0, 1/2]   {8, 9}   {10}   {11}
[1/2, 1/4, 1/4, 1/4]   {5, 10}   {8, 9}   {11}
[1/2, 1/4, 0, 1/2]   {8, 10}   {9}   {11}
[1/2, 1/2, 0, 1/4]   {9, 10}   {8}   {11}
[1/4, 5/8, 0, 1/4]   {8, 9, 10}   {}   {11}
[1/4, 1/4, 1/4, 1/4]   {8, 9, 10}   {11}   {12}
[0, 0, 1/2, 0]   {11}   {12}   {}
[0, 0, 0, 0]   {12}   {}   {}
                                [2, 5, 3, 5, 1]

                                      2       3      4
                         2 + 5 q + 7 q  + 11 q  + 9 q

# representatives from the maximal psd cells
# Format: fund.wt.coords  co-dim  J  <1  =1  >1

[0, 0, 0, 0]   0   {}   {12}   {}   {}
[1/4, 5/8, 0, 1/4]   0   {}   {8, 9, 10}   {}   {11}
[1/4, 1/4, 3/4, 1/4]   3   {}   {1, 2, 3, 4}   {5, 6, 7}   {8, 9, 10}
[1, 3/4, 1/4, 3/4]   3   {}   {2, 3, 4}   {1, 6, 7}   {5, 10}
[1/4, 1, 3/4, 1/4]   3   {}   {1, 3, 4}   {2, 5, 7}   {6, 9}
[1/4, 1/4, 3/4, 1]   3   {}   {1, 2, 3}   {4, 5, 6}   {7, 8}
[1, 1, 1, 1]   4   {}   {}   {1, 2, 3, 4}   {5, 6, 7}