C3

# point representatives from the cells that are positive
# semi-definite in the reflection representation

face   {1, 2, 3}

                                  [0, 0, 0, 0]

face   {2, 3}

[1/2, 0, 0]   {1}   {5}   {}
                                  [0, 0, 0, 1]

face   {1, 3}

[0, 1, 0]   {}   {2}   {9}
                                  [0, 0, 0, 1]

face   {3}

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

face   {1, 2}

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

face   {2}

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

face   {1}

[0, 1, 1]   {}   {2, 3}   {6}
[0, 1, 1/4]   {3}   {2}   {6}
[0, 1/4, 3/4]   {2, 3}   {6}   {9}
                                  [0, 0, 2, 1]

face   {}

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

                                           2      3
                            4 + 12 q + 15 q  + 8 q

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

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