old system 0
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,2,4,8}{1,5,9,7}{3,6,10}
{0,4,9,6}{1,3,5,8}{2,7,10}
{0,5,2,9}{1,6,4,10}{3,7,8}
{0,7,5,10}{1,4,3,9}{2,6,8}
is isomorphic to new system 8
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,2,4,8}{1,5,9,6}{3,7,10}
{0,4,3,5}{2,8,6,10}{1,7,9}
{0,6,3,9}{2,5,8,7}{1,4,10}
{0,7,5,10}{2,6,4,9}{1,3,8}
  0  1  2  3  4  5  6  7  8  9 10
  5  2  7  8  0  6  3  9 10  4  1
r0->r3 r1->r4 r2->r2 r3->r0 r4->r1 
[c1->c2,c2->c1,c3->c3,c1:0123->1032,c2:0123->0123,c3:012->210]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->0123,c3:012->210]
[c1->c1,c2->c2,c3->c3,c1:0123->3012,c2:0123->0123,c3:012->120]
[c1->c2,c2->c1,c3->c3,c1:0123->1230,c2:0123->2301,c3:012->012]
[c1->c2,c2->c1,c3->c3,c1:0123->1230,c2:0123->1032,c3:012->102]