THE FOLLOWING TWO CATERPILLARS ARE UNIQUELY DEFINED (UP TO INVERSION SYMMETRY)!
01234
41230
-- betweenness Triplets --
-- Format (a,b,c) which means that b should be between a and c.
0 1 2
0 1 3
0 1 4
0 2 1
0 2 3
0 2 4
0 3 1
0 3 2
0 3 4
1 2 3
1 2 4
1 3 4
2 1 4
2 3 4
3 1 4
3 2 4