list simplexSymmetryGroup = permutationFromIntvec(intvec( 1 .. 10 )),
permutationFromIntvec(intvec( 1, 2, 4, 3, 5, 7, 6, 9, 8, 10 )),
permutationFromIntvec(intvec( 1, 3, 2, 4, 6, 5, 7, 8, 10, 9 )),
permutationFromIntvec(intvec( 1, 3, 4, 2, 6, 7, 5, 10, 8, 9 )),
permutationFromIntvec(intvec( 1, 4, 2, 3, 7, 5, 6, 9, 10, 8 )),
permutationFromIntvec(intvec( 1, 4, 3, 2, 7, 6, 5, 10, 9, 8 )),
permutationFromIntvec(intvec( 1, 5, 6, 7, 2, 3, 4, 8, 9, 10 )),
permutationFromIntvec(intvec( 1, 5, 7, 6, 2, 4, 3, 9, 8, 10 )),
permutationFromIntvec(intvec( 1, 6, 5, 7, 3, 2, 4, 8, 10, 9 )),
permutationFromIntvec(intvec( 1, 6, 7, 5, 3, 4, 2, 10, 8, 9 )),
permutationFromIntvec(intvec( 1, 7, 5, 6, 4, 2, 3, 9, 10, 8 )),
permutationFromIntvec(intvec( 1, 7, 6, 5, 4, 3, 2, 10, 9, 8 )),
permutationFromIntvec(intvec( 2, 1, 3, 4, 5, 8, 9, 6, 7, 10 )),
permutationFromIntvec(intvec( 2, 1, 4, 3, 5, 9, 8, 7, 6, 10 )),
permutationFromIntvec(intvec( 2, 3, 1, 4, 8, 5, 9, 6, 10, 7 )),
permutationFromIntvec(intvec( 2, 3, 4, 1, 8, 9, 5, 10, 6, 7 )),
permutationFromIntvec(intvec( 2, 4, 1, 3, 9, 5, 8, 7, 10, 6 )),
permutationFromIntvec(intvec( 2, 4, 3, 1, 9, 8, 5, 10, 7, 6 )),
permutationFromIntvec(intvec( 2, 5, 8, 9, 1, 3, 4, 6, 7, 10 )),
permutationFromIntvec(intvec( 2, 5, 9, 8, 1, 4, 3, 7, 6, 10 )),
permutationFromIntvec(intvec( 2, 8, 5, 9, 3, 1, 4, 6, 10, 7 )),
permutationFromIntvec(intvec( 2, 8, 9, 5, 3, 4, 1, 10, 6, 7 )),
permutationFromIntvec(intvec( 2, 9, 5, 8, 4, 1, 3, 7, 10, 6 )),
permutationFromIntvec(intvec( 2, 9, 8, 5, 4, 3, 1, 10, 7, 6 )),
permutationFromIntvec(intvec( 3, 1, 2, 4, 6, 8, 10, 5, 7, 9 )),
permutationFromIntvec(intvec( 3, 1, 4, 2, 6, 10, 8, 7, 5, 9 )),
permutationFromIntvec(intvec( 3, 2, 1, 4, 8, 6, 10, 5, 9, 7 )),
permutationFromIntvec(intvec( 3, 2, 4, 1, 8, 10, 6, 9, 5, 7 )),
permutationFromIntvec(intvec( 3, 4, 1, 2, 10, 6, 8, 7, 9, 5 )),
permutationFromIntvec(intvec( 3, 4, 2, 1, 10, 8, 6, 9, 7, 5 )),
permutationFromIntvec(intvec( 3, 6, 8, 10, 1, 2, 4, 5, 7, 9 )),
permutationFromIntvec(intvec( 3, 6, 10, 8, 1, 4, 2, 7, 5, 9 )),
permutationFromIntvec(intvec( 3, 8, 6, 10, 2, 1, 4, 5, 9, 7 )),
permutationFromIntvec(intvec( 3, 8, 10, 6, 2, 4, 1, 9, 5, 7 )),
permutationFromIntvec(intvec( 3, 10, 6, 8, 4, 1, 2, 7, 9, 5 )),
permutationFromIntvec(intvec( 3, 10, 8, 6, 4, 2, 1, 9, 7, 5 )),
permutationFromIntvec(intvec( 4, 1, 2, 3, 7, 9, 10, 5, 6, 8 )),
permutationFromIntvec(intvec( 4, 1, 3, 2, 7, 10, 9, 6, 5, 8 )),
permutationFromIntvec(intvec( 4, 2, 1, 3, 9, 7, 10, 5, 8, 6 )),
permutationFromIntvec(intvec( 4, 2, 3, 1, 9, 10, 7, 8, 5, 6 )),
permutationFromIntvec(intvec( 4, 3, 1, 2, 10, 7, 9, 6, 8, 5 )),
permutationFromIntvec(intvec( 4, 3, 2, 1, 10, 9, 7, 8, 6, 5 )),
permutationFromIntvec(intvec( 4, 7, 9, 10, 1, 2, 3, 5, 6, 8 )),
permutationFromIntvec(intvec( 4, 7, 10, 9, 1, 3, 2, 6, 5, 8 )),
permutationFromIntvec(intvec( 4, 9, 7, 10, 2, 1, 3, 5, 8, 6 )),
permutationFromIntvec(intvec( 4, 9, 10, 7, 2, 3, 1, 8, 5, 6 )),
permutationFromIntvec(intvec( 4, 10, 7, 9, 3, 1, 2, 6, 8, 5 )),
permutationFromIntvec(intvec( 4, 10, 9, 7, 3, 2, 1, 8, 6, 5 )),
permutationFromIntvec(intvec( 5, 1, 6, 7, 2, 8, 9, 3, 4, 10 )),
permutationFromIntvec(intvec( 5, 1, 7, 6, 2, 9, 8, 4, 3, 10 )),
permutationFromIntvec(intvec( 5, 2, 8, 9, 1, 6, 7, 3, 4, 10 )),
permutationFromIntvec(intvec( 5, 2, 9, 8, 1, 7, 6, 4, 3, 10 )),
permutationFromIntvec(intvec( 5, 6, 1, 7, 8, 2, 9, 3, 10, 4 )),
permutationFromIntvec(intvec( 5, 6, 7, 1, 8, 9, 2, 10, 3, 4 )),
permutationFromIntvec(intvec( 5, 7, 1, 6, 9, 2, 8, 4, 10, 3 )),
permutationFromIntvec(intvec( 5, 7, 6, 1, 9, 8, 2, 10, 4, 3 )),
permutationFromIntvec(intvec( 5, 8, 2, 9, 6, 1, 7, 3, 10, 4 )),
permutationFromIntvec(intvec( 5, 8, 9, 2, 6, 7, 1, 10, 3, 4 )),
permutationFromIntvec(intvec( 5, 9, 2, 8, 7, 1, 6, 4, 10, 3 )),
permutationFromIntvec(intvec( 5, 9, 8, 2, 7, 6, 1, 10, 4, 3 )),
permutationFromIntvec(intvec( 6, 1, 5, 7, 3, 8, 10, 2, 4, 9 )),
permutationFromIntvec(intvec( 6, 1, 7, 5, 3, 10, 8, 4, 2, 9 )),
permutationFromIntvec(intvec( 6, 3, 8, 10, 1, 5, 7, 2, 4, 9 )),
permutationFromIntvec(intvec( 6, 3, 10, 8, 1, 7, 5, 4, 2, 9 )),
permutationFromIntvec(intvec( 6, 5, 1, 7, 8, 3, 10, 2, 9, 4 )),
permutationFromIntvec(intvec( 6, 5, 7, 1, 8, 10, 3, 9, 2, 4 )),
permutationFromIntvec(intvec( 6, 7, 1, 5, 10, 3, 8, 4, 9, 2 )),
permutationFromIntvec(intvec( 6, 7, 5, 1, 10, 8, 3, 9, 4, 2 )),
permutationFromIntvec(intvec( 6, 8, 3, 10, 5, 1, 7, 2, 9, 4 )),
permutationFromIntvec(intvec( 6, 8, 10, 3, 5, 7, 1, 9, 2, 4 )),
permutationFromIntvec(intvec( 6, 10, 3, 8, 7, 1, 5, 4, 9, 2 )),
permutationFromIntvec(intvec( 6, 10, 8, 3, 7, 5, 1, 9, 4, 2 )),
permutationFromIntvec(intvec( 7, 1, 5, 6, 4, 9, 10, 2, 3, 8 )),
permutationFromIntvec(intvec( 7, 1, 6, 5, 4, 10, 9, 3, 2, 8 )),
permutationFromIntvec(intvec( 7, 4, 9, 10, 1, 5, 6, 2, 3, 8 )),
permutationFromIntvec(intvec( 7, 4, 10, 9, 1, 6, 5, 3, 2, 8 )),
permutationFromIntvec(intvec( 7, 5, 1, 6, 9, 4, 10, 2, 8, 3 )),
permutationFromIntvec(intvec( 7, 5, 6, 1, 9, 10, 4, 8, 2, 3 )),
permutationFromIntvec(intvec( 7, 6, 1, 5, 10, 4, 9, 3, 8, 2 )),
permutationFromIntvec(intvec( 7, 6, 5, 1, 10, 9, 4, 8, 3, 2 )),
permutationFromIntvec(intvec( 7, 9, 4, 10, 5, 1, 6, 2, 8, 3 )),
permutationFromIntvec(intvec( 7, 9, 10, 4, 5, 6, 1, 8, 2, 3 )),
permutationFromIntvec(intvec( 7, 10, 4, 9, 6, 1, 5, 3, 8, 2 )),
permutationFromIntvec(intvec( 7, 10, 9, 4, 6, 5, 1, 8, 3, 2 )),
permutationFromIntvec(intvec( 8, 2, 5, 9, 3, 6, 10, 1, 4, 7 )),
permutationFromIntvec(intvec( 8, 2, 9, 5, 3, 10, 6, 4, 1, 7 )),
permutationFromIntvec(intvec( 8, 3, 6, 10, 2, 5, 9, 1, 4, 7 )),
permutationFromIntvec(intvec( 8, 3, 10, 6, 2, 9, 5, 4, 1, 7 )),
permutationFromIntvec(intvec( 8, 5, 2, 9, 6, 3, 10, 1, 7, 4 )),
permutationFromIntvec(intvec( 8, 5, 9, 2, 6, 10, 3, 7, 1, 4 )),
permutationFromIntvec(intvec( 8, 6, 3, 10, 5, 2, 9, 1, 7, 4 )),
permutationFromIntvec(intvec( 8, 6, 10, 3, 5, 9, 2, 7, 1, 4 )),
permutationFromIntvec(intvec( 8, 9, 2, 5, 10, 3, 6, 4, 7, 1 )),
permutationFromIntvec(intvec( 8, 9, 5, 2, 10, 6, 3, 7, 4, 1 )),
permutationFromIntvec(intvec( 8, 10, 3, 6, 9, 2, 5, 4, 7, 1 )),
permutationFromIntvec(intvec( 8, 10, 6, 3, 9, 5, 2, 7, 4, 1 )),
permutationFromIntvec(intvec( 9, 2, 5, 8, 4, 7, 10, 1, 3, 6 )),
permutationFromIntvec(intvec( 9, 2, 8, 5, 4, 10, 7, 3, 1, 6 )),
permutationFromIntvec(intvec( 9, 4, 7, 10, 2, 5, 8, 1, 3, 6 )),
permutationFromIntvec(intvec( 9, 4, 10, 7, 2, 8, 5, 3, 1, 6 )),
permutationFromIntvec(intvec( 9, 5, 2, 8, 7, 4, 10, 1, 6, 3 )),
permutationFromIntvec(intvec( 9, 5, 8, 2, 7, 10, 4, 6, 1, 3 )),
permutationFromIntvec(intvec( 9, 7, 4, 10, 5, 2, 8, 1, 6, 3 )),
permutationFromIntvec(intvec( 9, 7, 10, 4, 5, 8, 2, 6, 1, 3 )),
permutationFromIntvec(intvec( 9, 8, 2, 5, 10, 4, 7, 3, 6, 1 )),
permutationFromIntvec(intvec( 9, 8, 5, 2, 10, 7, 4, 6, 3, 1 )),
permutationFromIntvec(intvec( 9, 10, 4, 7, 8, 2, 5, 3, 6, 1 )),
permutationFromIntvec(intvec( 9, 10, 7, 4, 8, 5, 2, 6, 3, 1 )),
permutationFromIntvec(intvec( 10, 3, 6, 8, 4, 7, 9, 1, 2, 5 )),
permutationFromIntvec(intvec( 10, 3, 8, 6, 4, 9, 7, 2, 1, 5 )),
permutationFromIntvec(intvec( 10, 4, 7, 9, 3, 6, 8, 1, 2, 5 )),
permutationFromIntvec(intvec( 10, 4, 9, 7, 3, 8, 6, 2, 1, 5 )),
permutationFromIntvec(intvec( 10, 6, 3, 8, 7, 4, 9, 1, 5, 2 )),
permutationFromIntvec(intvec( 10, 6, 8, 3, 7, 9, 4, 5, 1, 2 )),
permutationFromIntvec(intvec( 10, 7, 4, 9, 6, 3, 8, 1, 5, 2 )),
permutationFromIntvec(intvec( 10, 7, 9, 4, 6, 8, 3, 5, 1, 2 )),
permutationFromIntvec(intvec( 10, 8, 3, 6, 9, 4, 7, 2, 5, 1 )),
permutationFromIntvec(intvec( 10, 8, 6, 3, 9, 7, 4, 5, 2, 1 )),
permutationFromIntvec(intvec( 10, 9, 4, 7, 8, 3, 6, 2, 5, 1 )),
permutationFromIntvec(intvec( 10, 9, 7, 4, 8, 6, 3, 5, 2, 1 ));