D4

# a list of representative points in the maximal cells

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