HAP_GCOMPLEX_SETUP:=[true];

HAP_GCOMPLEX_LIST:=


[
[rec(TheMatrixStab:=Group([  [[1,1],[-1,0]] ]), 
     TheRotSubgroup:=Group([  [[1,1],[-1,0]] ]), 
     BoundaryImage:=rec(ListIFace:=[], 
                        ListSign:=[],
                        ListElt:=[])),

rec(TheMatrixStab:=Group([  -IdentityMat(2), [[1,0],[0,1]] ]),
    TheRotSubgroup:=Group([ -IdentityMat(2), [[1,0],[0,1]] ]),
    BoundaryImage:=rec(ListIFace:=[],
                        ListSign:=[],
                        ListElt:=[]))
],
[rec(TheMatrixStab:=Group([ [[0,1],[-1,0]] ]), 
     TheRotSubgroup:=Group([-IdentityMat(2)]),
     BoundaryImage:=rec(ListIFace:=[1,1],
                        ListSign:=[1,-1],
                        #ListElt:=[IdentityMat(2), [[0,1],[-1,0]] ])),
                        ListElt:=[IdentityMat(2), [[1,-1],[0,1]] ])),

rec(TheMatrixStab:=Group([ -IdentityMat(2) ]),
     TheRotSubgroup:=Group([-IdentityMat(2)]),
     BoundaryImage:=rec(ListIFace:=[2,1],
                        ListSign:=[1,-1],
                        ListElt:=[IdentityMat(2), IdentityMat(2) ])),

rec(TheMatrixStab:=Group([ -IdentityMat(2) ]),
     TheRotSubgroup:=Group([-IdentityMat(2) ]),
     BoundaryImage:=rec(ListIFace:=[2,2],
                        ListSign:=[1,-1],
                        ListElt:=[IdentityMat(2), [[1,-1],[0,1]] ]))
],
[
rec(TheMatrixStab:=Group([ -[[1,0],[0,1]] ]),
     TheRotSubgroup:=Group([-[[1,0],[0,1]] ]),
     BoundaryImage:=rec(ListIFace:=[2,3,2,1],
                        ListSign:=[1,-1,-1,1],
                        ListElt:=[IdentityMat(2), IdentityMat(2), 
                                  [[1,-1],[0,1]], [[1,0],[0,1]] ]))
]];

HAP_GCOMPLEX_LIST[1][2].TheMatrixStab!.gname:="sl2inf";