Supplementary

Maximally inflected quintics

See also Frank’s page

Curve namePicture of a representativeTableauWebNum solitary pointsPromotion orderDihedral orbits
vendetta
1  2  3
4  5  6
7  8  9
63
[[[1, 2, 3], [4, 5, 6], [7, 8, 9]],  
[[1, 3, 4], [2, 6, 7], [5, 8, 9]],
[[1, 2, 5], [3, 4, 8], [6, 7, 9]]]
the mesa
1  2  7
3  4  8
5  6  9
49
[[[1, 2, 7], [3, 4, 8], [5, 6, 9]],
[[1, 4, 5], [2, 6, 7], [3, 8, 9]],
[[1, 2, 3], [4, 5, 8], [6, 7, 9]],
[[1, 2, 6], [3, 5, 8], [4, 7, 9]],
[[1, 3, 4], [2, 5, 6], [7, 8, 9]],
[[1, 2, 3], [4, 6, 7], [5, 8, 9]],
[[1, 3, 4], [2, 5, 8], [6, 7, 9]],
[[1, 2, 5], [3, 4, 6], [7, 8, 9]],
[[1, 3, 6], [2, 5, 7], [4, 8, 9]]]
the mouse
1  2  7
3  5  8
4  6  9
39
[[[1, 2, 7], [3, 5, 8], [4, 6, 9]],
[[1, 4, 6], [2, 5, 7], [3, 8, 9]],
[[1, 2, 3], [4, 6, 8], [5, 7, 9]],
[[1, 3, 4], [2, 5, 7], [6, 8, 9]],
[[1, 4, 5], [2, 6, 8], [3, 7, 9]],
[[1, 2, 6], [3, 5, 7], [4, 8, 9]],
[[1, 3, 7], [2, 4, 8], [5, 6, 9]],
[[1, 2, 4], [3, 5, 8], [6, 7, 9]],
[[1, 3, 5], [2, 4, 6], [7, 8, 9]]]
missing no
1  3  6
2  5  8
4  7  9
59
[[[1, 3, 6], [2, 5, 8], [4, 7, 9]],
[[1, 2, 4], [3, 6, 7], [5, 8, 9]],
[[1, 3, 5], [2, 4, 8], [6, 7, 9]],
[[1, 2, 4], [3, 5, 6], [7, 8, 9]],
[[1, 3, 5], [2, 6, 7], [4, 8, 9]],
[[1, 2, 6], [3, 4, 8], [5, 7, 9]],
[[1, 2, 3], [4, 5, 7], [6, 8, 9]],
[[1, 3, 4], [2, 6, 8], [5, 7, 9]],
[[1, 2, 5], [3, 4, 7], [6, 8, 9]]]
Ben Lomond
1  3  7
2  5  8
4  6  9
49
[[[1, 3, 7], [2, 5, 8], [4, 6, 9]],
[[1, 4, 6], [2, 5, 8], [3, 7, 9]],
[[1, 2, 4], [3, 6, 8], [5, 7, 9]],
[[1, 2, 5], [3, 6, 7], [4, 8, 9]],
[[1, 3, 5], [2, 4, 7], [6, 8, 9]],
[[1, 3, 6], [2, 4, 8], [5, 7, 9]],
[[1, 2, 4], [3, 5, 7], [6, 8, 9]],
[[1, 3, 5], [2, 6, 8], [4, 7, 9]],
[[1, 2, 6], [3, 4, 7], [5, 8, 9]]]
praying mantis
1  4  7
2  5  8
3  6  9
33
[[[1, 4, 7], [2, 5, 8], [3, 6, 9]],
[[1, 2, 5], [3, 6, 8], [4, 7, 9]],
[[1, 3, 6], [2, 4, 7], [5, 8, 9]]]