old system 1
{0,2,5}{1,6,10}{3,4,9,7,8}
{0,1,2,3}{4,5,6,7}{8,9,10}
{0,4,2,6}{1,8,5,9}{3,7,10}
{0,7,2,8}{1,4,10,5}{3,6,9}
{0,9,2,10}{1,3,5,7}{4,6,8}
is isomorphic to new system 1
{0,1,2}{3,4,5}{6,7,8,9,10}
{0,3,1,6}{2,4,8,10}{5,7,9}
{0,4,1,10}{2,7,3,9}{5,6,8}
{0,5,1,9}{2,6,3,8}{4,7,10}
{0,7,1,8}{2,3,10,5}{4,6,9}
  0  1  2  3  4  5  6  7  8  9 10
  1  3  0  6 10  2  4  8  7  9  5
r0->r0 r1->r1 r2->r2 r3->r4 r4->r3 
[c1->c1,c2->c2,c3->c3,c1:012->102,c2:012->012,c3:01234->0432]
[c1->c1,c2->c2,c3->c3,c1:0123->2103,c2:0123->3012,c3:012->120]
[c1->c1,c2->c2,c3->c3,c1:0123->2301,c2:0123->2103,c3:012->120]
[c1->c1,c2->c2,c3->c3,c1:0123->2301,c2:0123->1230,c3:012->102]
[c1->c1,c2->c2,c3->c3,c1:0123->2301,c2:0123->2103,c3:012->201]