old system 2
{1,6,8}{2,7,10}{0,4,3,5,9}
{1,4,10}{2,5,8}{0,6,9,3,7}
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,2,4,8}{1,5,7,9}{3,6,10}
{1,3,8,7}{2,6,4,9}{0,5,10}
is isomorphic to new system 7
{0,1,2}{3,4,5}{6,7,8,9,10}
{0,3,6}{1,4,8}{2,7,9,5,10}
{1,3,10,7}{2,5,8,6}{0,4,9}
{1,5,6,9}{2,3,7,4}{0,8,10}
{1,6,4,10}{2,8,3,9}{0,5,7}
  0  1  2  3  4  5  6  7  8  9 10
  7  1  3 10  2  5  8  6  4  9  0
r0->r1 r1->r0 r2->r2 r3->r3 r4->r4 
[c1->c2,c2->c1,c3->c3,c1:012->021,c2:012->120,c3:01234->1043]
[c1->c1,c2->c2,c3->c3,c1:012->120,c2:012->021,c3:01234->1234]
[c1->c1,c2->c2,c3->c3,c1:0123->3012,c2:0123->0123,c3:012->120]
[c1->c2,c2->c1,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->210]
[c1->c1,c2->c2,c3->c3,c1:0123->0321,c2:0123->2103,c3:012->210]