(* From exampletet3.nb. We solve the equations so that the rotations are of finite order according to tau values. These are traces of A12, A13,A14, A23, A24, A34. Since they fix a line, the conjugacy is determined by the traces only*)

Solve[{2-(1/beta34)-beta34+((2 d3)/beta34)==2+tau12,  2-(1/beta34)-beta34+((2 d2)/beta34)==2+ tau13,  2-(1/beta34)-beta34+((b3 c2)/beta34)==2+tau14,  2-(1/beta34)-beta34+((2 d1)/beta34)== 2+ tau23,  2-(1/beta34)-beta34+((a3 c1)/beta34)== 2+ tau24, 2-(1/beta34)+((a2 b1)/beta34)-beta34== 2+ tau34}, {d3, d2, c2, d1,a3,a2}]

(* solutions solved by beta34, b3,c1, b1 *)
(*tau's are fixed by angles of rotation *)