old system 1
{2,6,8}{3,4,9}{0,5,10,1,7}
{2,7,10}{3,5,8}{0,4,1,6,9}
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,2,4,8}{1,5,7,9}{3,6,10}
{0,6,4,10}{1,3,7,8}{2,5,9}
is isomorphic to new system 2
{0,1,2}{3,4,5}{6,7,8,9,10}
{0,3,6}{1,7,9}{2,4,10,5,8}
{0,5,1,10}{4,8,6,9}{2,3,7}
{0,8,3,9}{2,5,7,10}{1,4,6}
{1,3,10,8}{2,6,5,9}{0,4,7}
  0  1  2  3  4  5  6  7  8  9 10
  8 10  3  1  9  2  6  5  0  7  4
r0->r1 r1->r0 r2->r4 r3->r3 r4->r2 
[c1->c1,c2->c2,c3->c3,c1:012->120,c2:012->021,c3:01234->4012]
[c1->c2,c2->c1,c3->c3,c1:012->021,c2:012->120,c3:01234->2340]
[c1->c1,c2->c2,c3->c3,c1:0123->3210,c2:0123->3012,c3:012->021]
[c1->c1,c2->c2,c3->c3,c1:0123->1230,c2:0123->3012,c3:012->021]
[c1->c2,c2->c1,c3->c3,c1:0123->1230,c2:0123->3210,c3:012->102]