deg f census (OWR-15428-014).  Columns explained in the docstring.
FORMAT 2x2 (exhaustive, 1 orbits, 0s): {'patterns': 1, 'deg agreed (2-3 independent runs)': 1, 'deg <= multinomial bound': 1, 'unimodular': 1, 'tropical formula agrees': 1, 'reduced (k=1)': 1, 'deg = W + deg Den': 1, 'corner patterns': 1, 'corner: deg = n(n-1)': 1, 'matrix: deg = 2 + 2 #pinned': 1}
   degree distribution: {2: 1}
   max degree 2, multinomial bound 2
     deg  2  pinned 0  corner  E=[(0, 0), (1, 1)]  W=2 Den=0 coord={} noncoord=0
FORMAT 2x3 (exhaustive, 1 orbits, 0s): {'patterns': 1, 'deg agreed (2-3 independent runs)': 1, 'deg <= multinomial bound': 1, 'unimodular': 1, 'tropical formula agrees': 1, 'reduced (k=1)': 1, 'deg = W + deg Den': 1, 'corner patterns': 1, 'corner: deg = n(n-1)': 1, 'matrix: deg = 2 + 2 #pinned': 1}
   degree distribution: {2: 1}
   max degree 2, multinomial bound 3
     deg  2  pinned 0  corner  E=[(0, 0), (0, 1), (1, 2)]  W=2 Den=0 coord={} noncoord=0
FORMAT 2x4 (exhaustive, 2 orbits, 0s): {'patterns': 2, 'deg agreed (2-3 independent runs)': 2, 'deg <= multinomial bound': 2, 'unimodular': 2, 'tropical formula agrees': 2, 'reduced (k=1)': 2, 'deg = W + deg Den': 2, 'corner patterns': 1, 'corner: deg = n(n-1)': 1, 'matrix: deg = 2 + 2 #pinned': 2}
   degree distribution: {2: 2}
   max degree 2, multinomial bound 4
     deg  2  pinned 0  corner  E=[(0, 0), (0, 1), (0, 2), (1, 3)]  W=2 Den=0 coord={} noncoord=0
     deg  2  pinned 0          E=[(0, 0), (0, 1), (1, 2), (1, 3)]  W=2 Den=0 coord={} noncoord=0
FORMAT 2x5 (exhaustive, 2 orbits, 0s): {'patterns': 2, 'deg agreed (2-3 independent runs)': 2, 'deg <= multinomial bound': 2, 'unimodular': 2, 'tropical formula agrees': 2, 'reduced (k=1)': 2, 'deg = W + deg Den': 2, 'corner patterns': 1, 'corner: deg = n(n-1)': 1, 'matrix: deg = 2 + 2 #pinned': 2}
   degree distribution: {2: 2}
   max degree 2, multinomial bound 5
     deg  2  pinned 0  corner  E=[(0, 0), (0, 1), (0, 2), (0, 3), (1, 4)]  W=2 Den=0 coord={} noncoord=0
     deg  2  pinned 0          E=[(0, 0), (0, 1), (0, 2), (1, 3), (1, 4)]  W=2 Den=0 coord={} noncoord=0
FORMAT 3x3 (exhaustive, 2 orbits, 0s): {'patterns': 2, 'deg agreed (2-3 independent runs)': 2, 'deg <= multinomial bound': 2, 'unimodular': 2, 'tropical formula agrees': 2, 'reduced (k=1)': 2, 'deg = W + deg Den': 2, 'matrix: deg = 2 + 2 #pinned': 2, 'corner patterns': 1, 'corner: deg = n(n-1)': 1}
   degree distribution: {2: 1, 4: 1}
   max degree 4, multinomial bound 6
     deg  2  pinned 0  corner  E=[(0, 0), (0, 1), (1, 2), (2, 2)]  W=2 Den=0 coord={} noncoord=0
     deg  4  pinned 1          E=[(0, 0), (0, 1), (1, 0), (2, 2)]  W=2 Den=2 coord={(0, 0): 2} noncoord=0
FORMAT 3x4 (exhaustive, 4 orbits, 0s): {'patterns': 4, 'deg agreed (2-3 independent runs)': 4, 'deg <= multinomial bound': 4, 'unimodular': 4, 'tropical formula agrees': 4, 'reduced (k=1)': 4, 'deg = W + deg Den': 4, 'matrix: deg = 2 + 2 #pinned': 4, 'corner patterns': 1, 'corner: deg = n(n-1)': 1}
   degree distribution: {2: 1, 4: 2, 6: 1}
   max degree 6, multinomial bound 10
     deg  2  pinned 0  corner  E=[(0, 0), (0, 1), (0, 2), (1, 3), (2, 3)]  W=2 Den=0 coord={} noncoord=0
     deg  4  pinned 1          E=[(0, 0), (0, 1), (0, 2), (1, 0), (2, 3)]  W=2 Den=2 coord={(0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0), (0, 1), (1, 0), (2, 2), (2, 3)]  W=2 Den=2 coord={(0, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0), (0, 1), (1, 0), (1, 2), (2, 3)]  W=2 Den=4 coord={(0, 0): 2, (1, 0): 2} noncoord=0
FORMAT 3x5 (exhaustive, 6 orbits, 2s): {'patterns': 6, 'deg agreed (2-3 independent runs)': 6, 'deg <= multinomial bound': 6, 'unimodular': 6, 'tropical formula agrees': 6, 'reduced (k=1)': 6, 'deg = W + deg Den': 6, 'matrix: deg = 2 + 2 #pinned': 6, 'corner patterns': 1, 'corner: deg = n(n-1)': 1}
   degree distribution: {2: 1, 4: 3, 6: 2}
   max degree 6, multinomial bound 15
     deg  2  pinned 0  corner  E=[(0, 0), (0, 1), (0, 2), (0, 3), (1, 4), (2, 4)]  W=2 Den=0 coord={} noncoord=0
     deg  4  pinned 1          E=[(0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (2, 4)]  W=2 Den=2 coord={(0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0), (0, 1), (0, 2), (1, 0), (2, 3), (2, 4)]  W=2 Den=2 coord={(0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0), (0, 1), (0, 2), (1, 3), (1, 4), (2, 3)]  W=2 Den=2 coord={(1, 3): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0), (0, 1), (0, 2), (1, 0), (1, 3), (2, 4)]  W=2 Den=4 coord={(0, 0): 2, (1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0), (0, 1), (1, 0), (1, 2), (2, 3), (2, 4)]  W=2 Den=4 coord={(0, 0): 2, (1, 0): 2} noncoord=0
FORMAT 4x4 (exhaustive, 7 orbits, 6s): {'patterns': 7, 'deg agreed (2-3 independent runs)': 7, 'deg <= multinomial bound': 7, 'unimodular': 7, 'tropical formula agrees': 7, 'reduced (k=1)': 7, 'deg = W + deg Den': 7, 'matrix: deg = 2 + 2 #pinned': 7, 'corner patterns': 1, 'corner: deg = n(n-1)': 1}
   degree distribution: {2: 1, 4: 2, 6: 3, 8: 1}
   max degree 8, multinomial bound 20
     deg  2  pinned 0  corner  E=[(0, 0), (0, 1), (0, 2), (1, 3), (2, 3), (3, 3)]  W=2 Den=0 coord={} noncoord=0
     deg  4  pinned 1          E=[(0, 0), (0, 1), (0, 2), (1, 0), (2, 0), (3, 3)]  W=2 Den=2 coord={(0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0), (0, 1), (0, 2), (1, 0), (2, 3), (3, 3)]  W=2 Den=2 coord={(0, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0), (0, 1), (0, 2), (1, 0), (2, 1), (3, 3)]  W=2 Den=4 coord={(0, 0): 2, (0, 1): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0), (0, 1), (1, 0), (1, 2), (2, 3), (3, 3)]  W=2 Den=4 coord={(0, 0): 2, (1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0), (0, 1), (1, 0), (2, 2), (2, 3), (3, 2)]  W=2 Den=4 coord={(0, 0): 2, (2, 2): 2} noncoord=0
     deg  8  pinned 3          E=[(0, 0), (0, 1), (1, 0), (1, 2), (2, 1), (3, 3)]  W=2 Den=6 coord={(0, 0): 2, (0, 1): 2, (1, 0): 2} noncoord=0
FORMAT 2x2x2 (exhaustive, 2 orbits, 0s): {'patterns': 2, 'deg agreed (2-3 independent runs)': 2, 'deg <= multinomial bound': 2, 'unimodular': 2, 'tropical formula agrees': 2, 'reduced (k=1)': 2, 'deg = W + deg Den': 2, 'corner patterns': 1, 'corner: deg = n(n-1)': 1}
   degree distribution: {4: 1, 6: 1}
   max degree 6, multinomial bound 6
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (1, 1, 0)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  6  pinned 0  corner  E=[(0, 0, 0), (0, 1, 1), (1, 0, 1)]  W=3 Den=3 coord={(0, 0, 0): 1, (0, 1, 1): 1, (1, 0, 1): 1} noncoord=0
FORMAT 2x2x3 (exhaustive, 9 orbits, 1s): {'patterns': 9, 'deg agreed (2-3 independent runs)': 9, 'deg <= multinomial bound': 9, 'unimodular': 9, 'tropical formula agrees': 9, 'reduced (k=1)': 9, 'deg = W + deg Den': 9, 'corner patterns': 1, 'corner: deg = n(n-1)': 1}
   degree distribution: {4: 3, 6: 4, 8: 1, 12: 1}
   max degree 12, multinomial bound 12
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (1, 1, 0)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 2)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 1, 2)]  W=2 Den=2 coord={(0, 1, 2): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 1, 2)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 0  corner  E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 2)]  W=3 Den=3 coord={(0, 1, 2): 1, (1, 0, 2): 1} noncoord=1
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (1, 1, 0), (1, 1, 2)]  W=2 Den=4 coord={(0, 0, 0): 2, (1, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 1, 0), (1, 0, 1), (1, 1, 2)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  8  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 1, 0)]  W=3 Den=5 coord={(0, 0, 0): 3, (0, 1, 2): 1, (1, 1, 0): 1} noncoord=0
     deg 12  pinned 2          E=[(0, 0, 0), (0, 1, 1), (1, 0, 1), (1, 1, 2)]  W=4 Den=8 coord={(0, 0, 0): 1, (0, 1, 1): 3, (1, 0, 1): 3, (1, 1, 2): 1} noncoord=0
FORMAT 2x2x4 (exhaustive, 16 orbits, 3s): {'patterns': 16, 'deg agreed (2-3 independent runs)': 16, 'deg <= multinomial bound': 16, 'unimodular': 16, 'tropical formula agrees': 16, 'reduced (k=1)': 16, 'deg = W + deg Den': 16, 'corner patterns': 1, 'corner: deg = n(n-1)': 1}
   degree distribution: {4: 4, 6: 7, 8: 2, 10: 1, 12: 1, 13: 1}
   max degree 13, multinomial bound 20
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (1, 1, 0)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (1, 0, 3)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (1, 1, 3)]  W=2 Den=2 coord={(0, 1, 3): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 2), (1, 0, 3)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (1, 1, 3)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 0  corner  E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (1, 0, 3)]  W=3 Den=3 coord={(0, 1, 3): 1, (1, 0, 3): 1} noncoord=1
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (1, 1, 0), (1, 1, 3)]  W=2 Den=4 coord={(0, 0, 0): 2, (1, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 2), (1, 0, 3)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 2), (1, 1, 3)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 1, 2), (1, 1, 3)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 2)]  W=2 Den=4 coord={(0, 1, 2): 2, (1, 1, 2): 2} noncoord=0
     deg  8  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (1, 1, 0)]  W=3 Den=5 coord={(0, 0, 0): 3, (0, 1, 3): 1, (1, 1, 0): 1} noncoord=0
     deg  8  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (0, 1, 3), (1, 0, 2)]  W=3 Den=5 coord={(0, 1, 2): 3, (1, 0, 2): 1} noncoord=1
     deg 10  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 1, 0), (1, 1, 3)]  W=3 Den=7 coord={(0, 0, 0): 3, (0, 1, 2): 1, (1, 1, 0): 3} noncoord=0
     deg 12  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 2), (1, 1, 3)]  W=4 Den=8 coord={(0, 1, 2): 3, (1, 0, 2): 3, (1, 1, 3): 1} noncoord=1
     deg 13  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 0)]  W=4 Den=9 coord={(0, 0, 0): 4, (0, 1, 2): 1, (1, 0, 3): 1, (1, 1, 0): 3} noncoord=0
FORMAT 2x3x3 (exhaustive, 39 orbits, 6s): {'patterns': 39, 'deg agreed (2-3 independent runs)': 39, 'deg <= multinomial bound': 39, 'unimodular': 38, 'tropical formula agrees': 38, 'reduced (k=1)': 38, 'deg = W + deg Den': 38, 'corner patterns': 1, 'corner: deg = n(n-1)': 1, 'non-unimodular': 1}
   degree distribution: {4: 3, 6: 11, 8: 11, 10: 5, 12: 4, 14: 3, 16: 1, 20: 1}
   max degree 20, multinomial bound 30
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (1, 2, 0)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (1, 1, 0), (1, 2, 0)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (0, 2, 2), (1, 0, 0)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (1, 2, 1)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 0, 1): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (1, 1, 0), (1, 2, 1)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 0, 1): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 2), (1, 2, 0)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 2, 2), (1, 0, 0)]  W=2 Den=4 coord={(0, 0, 0): 4} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 2, 2), (1, 0, 1)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 0, 1): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 2, 2), (1, 2, 2)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 2, 2): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 2), (1, 2, 2)]  W=2 Den=4 coord={(0, 0, 0): 2, (1, 0, 2): 2} noncoord=0
     deg  6  pinned 0  corner  E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (0, 2, 2), (1, 0, 2)]  W=3 Den=3 coord={(1, 0, 2): 1} noncoord=2
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 0), (1, 2, 0)]  W=2 Den=4 coord={(0, 0, 0): 2, (1, 0, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 0), (1, 2, 2)]  W=2 Den=4 coord={(0, 0, 0): 2, (1, 0, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 1, 2), (1, 2, 2)]  W=2 Den=4 coord={(0, 1, 2): 2, (1, 1, 2): 2} noncoord=0
     deg  8  pinned 3          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 2), (1, 2, 1)]  W=2 Den=6 coord={(0, 0, 0): 2, (0, 0, 1): 2, (0, 1, 0): 2} noncoord=0
     deg  8  pinned 3          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 2, 2), (1, 1, 1)]  W=2 Den=6 coord={(0, 0, 0): 2, (0, 0, 1): 2, (0, 1, 0): 2} noncoord=0
     deg  8  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (1, 2, 2)]  W=2 Den=6 coord={(0, 0, 0): 4, (1, 0, 0): 2} noncoord=0
     deg  8  pinned 3          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 1), (1, 2, 2)]  W=2 Den=6 coord={(0, 0, 0): 2, (0, 0, 1): 2, (1, 0, 1): 2} noncoord=0
     deg  8  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 2), (1, 2, 0)]  W=3 Den=5 coord={(0, 0, 0): 3, (1, 0, 2): 1, (1, 2, 0): 1} noncoord=0
     deg  8  pinned 3          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 1, 2), (1, 2, 2)]  W=2 Den=6 coord={(0, 0, 0): 2, (0, 1, 0): 2, (1, 1, 2): 2} noncoord=0
     deg  8  pinned 3          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 0), (1, 2, 1)]  W=2 Den=6 coord={(0, 0, 0): 2, (0, 0, 1): 2, (1, 0, 0): 2} noncoord=0
     deg  8  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 2), (1, 2, 2)]  W=3 Den=5 coord={(0, 1, 2): 1, (1, 0, 2): 3} noncoord=1
     deg  8  pinned 3          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 1, 2), (1, 2, 0)]  W=2 Den=6 coord={(0, 0, 0): 2, (0, 1, 2): 2, (1, 1, 2): 2} noncoord=0
     deg  8  pinned 3          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 2, 0), (1, 2, 2)]  W=2 Den=6 coord={(0, 0, 0): 2, (1, 2, 0): 2, (1, 2, 2): 2} noncoord=0
     deg  8  pinned 3          E=[(0, 0, 0), (0, 0, 1), (1, 0, 0), (1, 1, 1), (1, 2, 2)]  W=2 Den=6 coord={(0, 0, 0): 2, (0, 0, 1): 2, (1, 0, 0): 2} noncoord=0
     deg 10  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 2, 2), (1, 0, 2)]  W=3 Den=7 coord={(0, 0, 0): 4, (0, 2, 2): 1, (1, 0, 2): 1} noncoord=1
     deg 10  pinned 4          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 1, 1), (1, 2, 2)]  W=2 Den=8 coord={(0, 0, 0): 2, (0, 0, 1): 2, (0, 1, 0): 2, (1, 1, 1): 2} noncoord=0
     deg 10  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (0, 2, 2), (1, 1, 0)]  W=3 Den=7 coord={(0, 0, 0): 3, (0, 1, 2): 3, (1, 1, 0): 1} noncoord=0
     deg 10  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 1, 0), (1, 2, 0)]  W=3 Den=7 coord={(0, 0, 0): 3, (0, 1, 2): 1, (1, 1, 0): 3} noncoord=0
     deg 10  pinned 3          E=[(0, 0, 0), (0, 1, 1), (0, 2, 2), (1, 0, 0), (1, 1, 2)]  W=2 Den=8 coord={(0, 0, 0): 4, (1, 0, 0): 2, (1, 1, 2): 2} noncoord=0
     deg 12  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 2, 2), (1, 1, 2)]  W=3 Den=9 coord={(0, 0, 0): 3, (0, 1, 0): 3, (0, 2, 2): 1, (1, 1, 2): 1} noncoord=1
     deg 12  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 2), (1, 2, 1)]  W=3 Den=9 coord={(0, 0, 0): 4, (0, 0, 1): 3, (1, 0, 2): 1, (1, 2, 1): 1} noncoord=0
     deg 12  pinned 2          E=[(0, 0, 0), (0, 0, 1), (1, 0, 2), (1, 1, 0), (1, 2, 1)]  W=3 Den=9 coord={(0, 0, 0): 3, (0, 0, 1): 3, (1, 0, 2): 1} noncoord=2
     deg 12  pinned 4          E=[(0, 0, 0), (0, 1, 1), (0, 2, 2), (1, 0, 1), (1, 1, 0)]  NON-UNIMODULAR divisors=[1, 1, 1, 1, 2]
     deg 14  pinned 3          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 1, 2), (1, 2, 1)]  W=3 Den=11 coord={(0, 0, 0): 3, (0, 0, 1): 3, (0, 1, 0): 3, (1, 1, 2): 1, (1, 2, 1): 1} noncoord=0
     deg 14  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 2), (1, 2, 0)]  W=4 Den=10 coord={(0, 0, 0): 4, (0, 1, 2): 1, (1, 0, 2): 3, (1, 2, 0): 1} noncoord=1
     deg 14  pinned 3          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 1, 0), (1, 2, 1)]  W=3 Den=11 coord={(0, 0, 0): 3, (0, 0, 1): 4, (0, 1, 2): 1, (1, 1, 0): 3} noncoord=0
     deg 16  pinned 3          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 1, 0), (1, 2, 2)]  W=4 Den=12 coord={(0, 0, 0): 4, (0, 1, 2): 3, (1, 1, 0): 3, (1, 2, 2): 1} noncoord=1
     deg 20  pinned 3          E=[(0, 0, 0), (0, 1, 1), (0, 2, 2), (1, 0, 1), (1, 1, 2)]  W=5 Den=15 coord={(0, 0, 0): 2, (0, 1, 1): 3, (0, 2, 2): 2, (1, 0, 1): 4, (1, 1, 2): 4} noncoord=0
FORMAT 2x2x2x2 (exhaustive, 11 orbits, 3s): {'patterns': 11, 'deg agreed (2-3 independent runs)': 11, 'deg <= multinomial bound': 11, 'unimodular': 10, 'tropical formula agrees': 10, 'reduced (k=1)': 10, 'deg = W + deg Den': 10, 'corner patterns': 1, 'corner: deg = n(n-1)': 1, 'non-unimodular': 1}
   degree distribution: {6: 3, 8: 2, 9: 1, 11: 1, 12: 2, 14: 1, 18: 1}
   max degree 18, multinomial bound 24
     deg  6  pinned 1          E=[(0, 0, 0, 0), (0, 0, 0, 1), (0, 0, 1, 0), (1, 1, 0, 0)]  W=2 Den=4 coord={(0, 0, 0, 0): 4} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0, 0), (0, 0, 0, 1), (0, 0, 1, 0), (1, 1, 0, 1)]  W=2 Den=4 coord={(0, 0, 0, 0): 2, (0, 0, 0, 1): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0, 0), (0, 0, 0, 1), (0, 1, 1, 0), (1, 1, 1, 0)]  W=2 Den=4 coord={(0, 0, 0, 0): 2, (0, 1, 1, 0): 2} noncoord=0
     deg  8  pinned 3          E=[(0, 0, 0, 0), (0, 0, 0, 1), (0, 0, 1, 0), (1, 1, 1, 1)]  W=2 Den=6 coord={(0, 0, 0, 0): 2, (0, 0, 0, 1): 2, (0, 0, 1, 0): 2} noncoord=0
     deg  8  pinned 3          E=[(0, 0, 0, 0), (0, 0, 0, 1), (0, 1, 1, 0), (1, 1, 1, 1)]  W=2 Den=6 coord={(0, 0, 0, 0): 2, (0, 0, 0, 1): 2, (0, 1, 1, 0): 2} noncoord=0
     deg  9  pinned 1          E=[(0, 0, 0, 0), (0, 0, 0, 1), (0, 1, 1, 0), (1, 0, 1, 0)]  W=3 Den=6 coord={(0, 0, 0, 0): 4, (0, 1, 1, 0): 1, (1, 0, 1, 0): 1} noncoord=0
     deg 11  pinned 2          E=[(0, 0, 0, 0), (0, 0, 0, 1), (0, 1, 1, 0), (1, 0, 1, 1)]  W=3 Den=8 coord={(0, 0, 0, 0): 3, (0, 0, 0, 1): 3, (0, 1, 1, 0): 1, (1, 0, 1, 1): 1} noncoord=0
     deg 12  pinned 0  corner  E=[(0, 0, 0, 0), (0, 0, 1, 1), (0, 1, 0, 1), (1, 0, 0, 1)]  W=4 Den=8 coord={(0, 0, 0, 0): 2, (0, 0, 1, 1): 2, (0, 1, 0, 1): 2, (1, 0, 0, 1): 2} noncoord=0
     deg 12  pinned 4          E=[(0, 0, 0, 0), (0, 0, 1, 1), (1, 1, 0, 1), (1, 1, 1, 0)]  NON-UNIMODULAR divisors=[1, 1, 1, 2]
     deg 14  pinned 2          E=[(0, 0, 0, 0), (0, 0, 1, 1), (0, 1, 0, 1), (1, 0, 1, 0)]  W=4 Den=10 coord={(0, 0, 0, 0): 4, (0, 0, 1, 1): 4, (0, 1, 0, 1): 1, (1, 0, 1, 0): 1} noncoord=0
     deg 18  pinned 3          E=[(0, 0, 0, 0), (0, 0, 1, 1), (0, 1, 0, 1), (1, 1, 1, 0)]  W=5 Den=13 coord={(0, 0, 0, 0): 4, (0, 0, 1, 1): 4, (0, 1, 0, 1): 4, (1, 1, 1, 0): 1} noncoord=0
FORMAT 2x2x5 (exhaustive, 30 orbits, 22s): {'patterns': 30, 'deg agreed (2-3 independent runs)': 30, 'deg <= multinomial bound': 30, 'unimodular': 30, 'tropical formula agrees': 30, 'reduced (k=1)': 30, 'deg = W + deg Den': 30, 'corner patterns': 1, 'corner: deg = n(n-1)': 1}
   degree distribution: {4: 5, 6: 15, 8: 3, 10: 2, 12: 2, 13: 2, 14: 1}
   max degree 14, multinomial bound 30
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 0, 4), (1, 1, 0)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 1, 0), (1, 0, 4)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 1, 4), (1, 1, 4)]  W=2 Den=2 coord={(0, 1, 4): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (1, 0, 3), (1, 0, 4)]  W=2 Den=2 coord={(0, 0, 0): 2} noncoord=0
     deg  4  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (0, 1, 4), (1, 1, 3)]  W=2 Den=2 coord={(0, 1, 3): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 1, 0), (1, 1, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 0  corner  E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 1, 4), (1, 0, 4)]  W=3 Den=3 coord={(0, 1, 4): 1, (1, 0, 4): 1} noncoord=1
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (1, 1, 0), (1, 1, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (1, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (0, 1, 3), (1, 0, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (0, 1, 3), (1, 1, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (1, 0, 3), (1, 1, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (1, 1, 3), (1, 1, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (1, 0, 4), (1, 1, 3)]  W=2 Den=4 coord={(0, 1, 3): 2, (1, 1, 3): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (1, 1, 3), (1, 1, 4)]  W=2 Den=4 coord={(0, 1, 3): 2, (1, 1, 3): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (1, 1, 0), (1, 1, 3), (1, 1, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (1, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 2), (1, 0, 3), (1, 0, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 2), (1, 0, 3), (1, 1, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 2), (1, 0, 3), (1, 1, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 2), (1, 1, 3), (1, 1, 4)]  W=2 Den=4 coord={(0, 0, 0): 2, (0, 1, 0): 2} noncoord=0
     deg  6  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (0, 1, 3), (1, 0, 4), (1, 1, 4)]  W=2 Den=4 coord={(1, 0, 4): 2, (1, 1, 4): 2} noncoord=0
     deg  8  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 1, 4), (1, 1, 0)]  W=3 Den=5 coord={(0, 0, 0): 3, (0, 1, 4): 1, (1, 1, 0): 1} noncoord=0
     deg  8  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (0, 1, 4), (1, 0, 3)]  W=3 Den=5 coord={(0, 1, 3): 3, (1, 0, 3): 1} noncoord=1
     deg  8  pinned 1          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (0, 1, 4), (1, 1, 0)]  W=3 Den=5 coord={(0, 0, 0): 3, (1, 1, 0): 1} noncoord=1
     deg 10  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (1, 1, 0), (1, 1, 4)]  W=3 Den=7 coord={(0, 0, 0): 3, (0, 1, 3): 1, (1, 1, 0): 3} noncoord=0
     deg 10  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (0, 1, 3), (1, 0, 2), (1, 0, 4)]  W=3 Den=7 coord={(0, 1, 2): 3, (1, 0, 2): 3} noncoord=1
     deg 12  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (1, 0, 3), (1, 1, 4)]  W=4 Den=8 coord={(0, 1, 3): 3, (1, 0, 3): 3, (1, 1, 4): 1} noncoord=1
     deg 12  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 2), (1, 1, 3), (1, 1, 4)]  W=4 Den=8 coord={(0, 1, 2): 3, (1, 0, 2): 3} noncoord=2
     deg 13  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 3), (1, 0, 4), (1, 1, 0)]  W=4 Den=9 coord={(0, 0, 0): 4, (0, 1, 3): 1, (1, 0, 4): 1, (1, 1, 0): 3} noncoord=0
     deg 13  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (0, 1, 3), (1, 0, 2), (1, 1, 4)]  W=4 Den=9 coord={(0, 1, 2): 4, (1, 0, 2): 3, (1, 1, 4): 1} noncoord=1
     deg 14  pinned 2          E=[(0, 0, 0), (0, 0, 1), (0, 1, 2), (1, 0, 3), (1, 1, 0), (1, 1, 4)]  W=4 Den=10 coord={(0, 0, 0): 4, (0, 1, 2): 1, (1, 0, 3): 1, (1, 1, 0): 4} noncoord=0
FORMAT 2x2x2x3 (exhaustive, 122 orbits, 55s): {'patterns': 122, 'deg agreed (2-3 independent runs)': 122, 'deg <= multinomial bound': 122, 'unimodular': 117, 'tropical formula agrees': 117, 'reduced (k=1)': 117, 'deg = W + deg Den': 117, 'corner patterns': 1, 'corner: deg = n(n-1)': 1, 'non-unimodular': 5}
   degree distribution: {6: 10, 8: 26, 9: 3, 10: 17, 11: 7, 12: 7, 13: 7, 14: 7, 15: 6, 16: 5, 17: 2, 18: 6, 20: 5, 21: 2, 22: 4, 24: 3, 26: 2, 27: 1, 28: 1, 31: 1}
   max degree 31, multinomial bound 60
FORMAT 2x3x4 (exhaustive, 229 orbits, 93s): {'patterns': 229, 'deg agreed (2-3 independent runs)': 229, 'deg <= multinomial bound': 229, 'unimodular': 225, 'tropical formula agrees': 225, 'reduced (k=1)': 225, 'deg = W + deg Den': 225, 'corner patterns': 1, 'corner: deg = n(n-1)': 1, 'non-unimodular': 4}
   degree distribution: {4: 7, 6: 35, 8: 69, 10: 38, 12: 24, 14: 23, 15: 2, 16: 10, 17: 2, 18: 4, 19: 2, 20: 4, 21: 3, 22: 2, 23: 2, 25: 1, 30: 1}
   max degree 30, multinomial bound 60
FORMAT 4x5 (random sample of 200 admissible patterns, 20s): {'patterns': 200, 'deg agreed (2-3 independent runs)': 200, 'deg <= multinomial bound': 200, 'unimodular': 200, 'tropical formula agrees': 200, 'reduced (k=1)': 200, 'deg = W + deg Den': 200, 'matrix: deg = 2 + 2 #pinned': 200}
   degree distribution: {4: 14, 6: 77, 8: 94, 10: 15}
   max degree 10, multinomial bound 35
FORMAT 5x5 (random sample of 200 admissible patterns, 22s): {'patterns': 200, 'deg agreed (2-3 independent runs)': 200, 'deg <= multinomial bound': 200, 'unimodular': 200, 'tropical formula agrees': 200, 'reduced (k=1)': 200, 'deg = W + deg Den': 200, 'matrix: deg = 2 + 2 #pinned': 200}
   degree distribution: {4: 3, 6: 32, 8: 88, 10: 66, 12: 11}
   max degree 12, multinomial bound 70
FORMAT 3x3x3 (random sample of 600 admissible patterns, 147s): {'patterns': 600, 'deg agreed (2-3 independent runs)': 600, 'deg <= multinomial bound': 600, 'unimodular': 588, 'tropical formula agrees': 588, 'reduced (k=1)': 588, 'deg = W + deg Den': 588, 'non-unimodular': 12}
   degree distribution: {6: 16, 8: 95, 10: 140, 12: 73, 14: 61, 16: 70, 18: 72, 20: 21, 22: 5, 23: 2, 24: 17, 25: 4, 26: 8, 28: 5, 29: 5, 30: 1, 32: 2, 39: 3}
   max degree 39, multinomial bound 90
FORMAT 3x3x4 (random sample of 200 admissible patterns, 76s): {'patterns': 200, 'deg agreed (2-3 independent runs)': 200, 'deg <= multinomial bound': 200, 'unimodular': 192, 'tropical formula agrees': 192, 'reduced (k=1)': 192, 'deg = W + deg Den': 192, 'non-unimodular': 8}
   degree distribution: {6: 1, 8: 9, 10: 30, 12: 38, 14: 21, 16: 19, 18: 16, 20: 22, 21: 1, 22: 5, 23: 1, 24: 6, 25: 2, 26: 8, 27: 3, 28: 2, 29: 2, 30: 2, 32: 2, 33: 1, 34: 1, 35: 4, 38: 1, 42: 1, 43: 1, 48: 1}
   max degree 48, multinomial bound 210
FORMAT 2x2x2x2x2 (random sample of 300 admissible patterns, 132s): {'patterns': 300, 'deg agreed (2-3 independent runs)': 300, 'deg <= multinomial bound': 300, 'unimodular': 290, 'tropical formula agrees': 290, 'reduced (k=1)': 290, 'deg = W + deg Den': 290, 'non-unimodular': 10}
   degree distribution: {8: 12, 10: 49, 12: 34, 14: 35, 15: 8, 16: 22, 17: 17, 18: 17, 20: 12, 21: 9, 22: 15, 23: 4, 24: 7, 25: 6, 26: 5, 27: 8, 28: 1, 29: 8, 30: 9, 32: 4, 34: 4, 36: 7, 40: 4, 42: 1, 46: 2}
   max degree 46, multinomial bound 120
FORMAT 2x2x3x3 (random sample of 200 admissible patterns, 89s): {'patterns': 200, 'deg agreed (2-3 independent runs)': 200, 'deg <= multinomial bound': 200, 'unimodular': 184, 'tropical formula agrees': 184, 'reduced (k=1)': 184, 'deg = W + deg Den': 184, 'non-unimodular': 16}
   degree distribution: {8: 9, 10: 26, 11: 1, 12: 23, 13: 6, 14: 15, 15: 7, 16: 11, 17: 9, 18: 8, 19: 11, 20: 13, 21: 7, 22: 7, 23: 2, 24: 3, 25: 1, 26: 10, 28: 5, 29: 1, 30: 3, 31: 1, 32: 7, 33: 1, 34: 2, 35: 2, 38: 3, 40: 3, 43: 1, 44: 1, 50: 1}
   max degree 50, multinomial bound 180
FORMAT 3x4x5 (random sample of 60 admissible patterns, 49s): {'patterns': 60, 'deg agreed (2-3 independent runs)': 60, 'deg <= multinomial bound': 60, 'unimodular': 57, 'tropical formula agrees': 57, 'reduced (k=1)': 57, 'deg = W + deg Den': 57, 'non-unimodular': 3}
   degree distribution: {10: 2, 12: 1, 14: 7, 16: 8, 18: 4, 20: 5, 22: 3, 24: 2, 26: 2, 27: 1, 28: 1, 30: 5, 35: 1, 36: 2, 37: 2, 38: 1, 39: 3, 40: 1, 41: 1, 46: 1, 50: 1, 53: 1, 55: 1, 57: 1, 58: 1, 59: 1, 62: 1}
   max degree 62, multinomial bound 1260
FORMAT 2x2x2x2x2x2 (random sample of 60 admissible patterns, 157s): {'patterns': 60, 'deg agreed (2-3 independent runs)': 60, 'deg <= multinomial bound': 60, 'unimodular': 52, 'tropical formula agrees': 52, 'reduced (k=1)': 52, 'deg = W + deg Den': 52, 'non-unimodular': 8}
   degree distribution: {10: 1, 12: 2, 14: 3, 18: 3, 20: 3, 21: 1, 23: 1, 24: 4, 26: 2, 28: 3, 30: 2, 31: 3, 32: 4, 33: 1, 35: 2, 36: 3, 38: 1, 39: 2, 40: 1, 45: 1, 46: 2, 48: 1, 50: 1, 52: 1, 54: 1, 56: 1, 58: 2, 62: 1, 64: 1, 65: 1, 67: 1, 78: 1, 80: 1, 82: 1, 104: 1}
   max degree 104, multinomial bound 720
FORMAT 3x3x3x3 (random sample of 40 admissible patterns, 117s): {'patterns': 40, 'deg agreed (2-3 independent runs)': 40, 'deg <= multinomial bound': 40, 'unimodular': 36, 'tropical formula agrees': 36, 'reduced (k=1)': 36, 'deg = W + deg Den': 36, 'non-unimodular': 4}
   degree distribution: {14: 2, 16: 1, 18: 3, 22: 1, 24: 1, 28: 2, 29: 1, 32: 1, 34: 2, 36: 1, 37: 1, 40: 1, 42: 3, 46: 1, 48: 2, 50: 1, 51: 1, 52: 2, 54: 3, 56: 1, 58: 1, 64: 1, 76: 1, 82: 2, 85: 2, 98: 1, 122: 1}
   max degree 122, multinomial bound 2520
done
