HAP_GCOMPLEX_SETUP:=[false];
if IsBound(x) then HAP_GCOMPLEX_SETUP[2]:=x;fi;
x:=Sqrt(-5);

HAP_GCOMPLEX_LIST := [
[
rec( TheMatrixStab := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ 0, 1 ],[ -1, 0]]
,
[[ 0, -1 ],[ 1, 0]]
]),
TheRotSubgroup := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ 0, 1 ],[ -1, 0]]
,
[[ 0, -1 ],[ 1, 0]]
]),
BoundaryImage := rec( ListIFace:=[], ListSign:=[], ListElt:=[])
),
rec( TheMatrixStab := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ -2, -x ],[ -x, 2]]
,
[[ 2, x ],[ x, -2]]
,
[[ x, -2 ],[ -2, -x]]
,
[[ -x, 2 ],[ 2, x]]
,
[[ 0, 1 ],[ -1, 0]]
,
[[ 0, -1 ],[ 1, 0]]
]),
TheRotSubgroup := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ -2, -x ],[ -x, 2]]
,
[[ 2, x ],[ x, -2]]
,
[[ x, -2 ],[ -2, -x]]
,
[[ -x, 2 ],[ 2, x]]
,
[[ 0, 1 ],[ -1, 0]]
,
[[ 0, -1 ],[ 1, 0]]
]),
BoundaryImage := rec( ListIFace:=[], ListSign:=[], ListElt:=[])
),
rec( TheMatrixStab := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ -3, -2*x ],[ -x, 3]]
,
[[ 3, 2*x ],[ x, -3]]
,
[[ x, -2 ],[ -2, -x]]
,
[[ -x, 2 ],[ 2, x]]
,
[[ x, -4 ],[ -1, -x]]
,
[[ -x, 4 ],[ 1, x]]
]),
TheRotSubgroup := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ -3, -2*x ],[ -x, 3]]
,
[[ 3, 2*x ],[ x, -3]]
,
[[ x, -2 ],[ -2, -x]]
,
[[ -x, 2 ],[ 2, x]]
,
[[ x, -4 ],[ -1, -x]]
,
[[ -x, 4 ],[ 1, x]]
]),
BoundaryImage := rec( ListIFace:=[], ListSign:=[], ListElt:=[])
),
rec( TheMatrixStab := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 1 ],[ -1, 0]]
,
[[ -1, -1 ],[ 1, 0]]
,
[[ 0, 1 ],[ -1, -1]]
,
[[ 0, -1 ],[ 1, 1]]
]),
TheRotSubgroup := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 1 ],[ -1, 0]]
,
[[ -1, -1 ],[ 1, 0]]
,
[[ 0, 1 ],[ -1, -1]]
,
[[ 0, -1 ],[ 1, 1]]
]),
BoundaryImage := rec( ListIFace:=[], ListSign:=[], ListElt:=[])
),
rec( TheMatrixStab := Group([
[[ -x, -x + 2 ],[ 2, x + 2]]
,
[[ -x + 6, 2*x + 5 ],[ 2*x, x - 4]]
,
[[ -1, 0 ],[ 0, -1]]
]),
TheRotSubgroup := Group([
[[ -x, -x + 2 ],[ 2, x + 2]]
,
[[ -x + 6, 2*x + 5 ],[ 2*x, x - 4]]
,
[[ -1, 0 ],[ 0, -1]]
]),
BoundaryImage := rec( ListIFace:=[], ListSign:=[], ListElt:=[])
),
rec( TheMatrixStab := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 1 ],[ -1, 0]]
,
[[ -1, -1 ],[ 1, 0]]
,
[[ 0, 1 ],[ -1, -1]]
,
[[ 0, -1 ],[ 1, 1]]
]),
TheRotSubgroup := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 1 ],[ -1, 0]]
,
[[ -1, -1 ],[ 1, 0]]
,
[[ 0, 1 ],[ -1, -1]]
,
[[ 0, -1 ],[ 1, 1]]
]),
BoundaryImage := rec( ListIFace:=[], ListSign:=[], ListElt:=[])
),
rec( TheMatrixStab := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ -2, -x ],[ -x, 2]]
,
[[ 2, x ],[ x, -2]]
]),
TheRotSubgroup := Group([
[[ 1, 0 ],[ 0, 1]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ -2, -x ],[ -x, 2]]
,
[[ 2, x ],[ x, -2]]
]),
BoundaryImage := rec( ListIFace:=[], ListSign:=[], ListElt:=[])
),
],
[
rec( TheMatrixStab := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ 0, -1 ],[ 1, 0]]
,
[[ 0, 1 ],[ -1, 0]]
,
[[ 1, 0 ],[ 0, 1]]
]),
TheRotSubgroup := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ 0, -1 ],[ 1, 0]]
,
[[ 0, 1 ],[ -1, 0]]
,
[[ 1, 0 ],[ 0, 1]]
]),
BoundaryImage := rec(
ListIFace:=[ 1, 2],
 ListSign := [-1,1],
ListElt := [IdentityMat(2), IdentityMat(2)])
),
rec( TheMatrixStab := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 0 ],[ 0, 1]]
]),
TheRotSubgroup := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 0 ],[ 0, 1]]
]),
BoundaryImage := rec(
ListIFace:=[ 1, 4],
 ListSign := [-1,1],
ListElt := [IdentityMat(2), IdentityMat(2)])
),
rec( TheMatrixStab := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ -x, 4 ],[ 1, x]]
,
[[ x, -4 ],[ -1, -x]]
,
[[ 1, 0 ],[ 0, 1]]
]),
TheRotSubgroup := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ -x, 4 ],[ 1, x]]
,
[[ x, -4 ],[ -1, -x]]
,
[[ 1, 0 ],[ 0, 1]]
]),
BoundaryImage := rec(
ListIFace:=[ 1, 3],
 ListSign := [-1,1],
ListElt := [[[ -1, x ],[ 0, -1]], IdentityMat(2)])
),
rec( TheMatrixStab := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ -x, 2 ],[ 2, x]]
,
[[ x, -2 ],[ -2, -x]]
,
[[ 1, 0 ],[ 0, 1]]
]),
TheRotSubgroup := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ -x, 2 ],[ 2, x]]
,
[[ x, -2 ],[ -2, -x]]
,
[[ 1, 0 ],[ 0, 1]]
]),
BoundaryImage := rec(
ListIFace:=[ 2, 3],
 ListSign := [-1,1],
ListElt := [IdentityMat(2), IdentityMat(2)])
),
rec( TheMatrixStab := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ -2, -x ],[ -x, 2]]
,
[[ 1, 0 ],[ 0, 1]]
,
[[ 2, x ],[ x, -2]]
]),
TheRotSubgroup := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ -2, -x ],[ -x, 2]]
,
[[ 1, 0 ],[ 0, 1]]
,
[[ 2, x ],[ x, -2]]
]),
BoundaryImage := rec(
ListIFace:=[ 2, 7],
 ListSign := [-1,1],
ListElt := [IdentityMat(2), IdentityMat(2)])
),
rec( TheMatrixStab := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ -3, -2*x ],[ -x, 3]]
,
[[ 1, 0 ],[ 0, 1]]
,
[[ 3, 2*x ],[ x, -3]]
]),
TheRotSubgroup := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ -3, -2*x ],[ -x, 3]]
,
[[ 1, 0 ],[ 0, 1]]
,
[[ 3, 2*x ],[ x, -3]]
]),
BoundaryImage := rec(
ListIFace:=[ 3, 7],
 ListSign := [-1,1],
ListElt := [IdentityMat(2), [[ -3*x - 2, -2*x + 5 ],[ 5, 2*x + 2]]])
),
rec( TheMatrixStab := Group([
[[ -1, -1 ],[ 1, 0]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ 0, -1 ],[ 1, 1]]
,
[[ 0, 1 ],[ -1, -1]]
,
[[ 1, 0 ],[ 0, 1]]
,
[[ 1, 1 ],[ -1, 0]]
]),
TheRotSubgroup := Group([
[[ -1, -1 ],[ 1, 0]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ 0, -1 ],[ 1, 1]]
,
[[ 0, 1 ],[ -1, -1]]
,
[[ 1, 0 ],[ 0, 1]]
,
[[ 1, 1 ],[ -1, 0]]
]),
BoundaryImage := rec(
ListIFace:=[ 4, 6],
 ListSign := [-1,1],
ListElt := [IdentityMat(2), IdentityMat(2)])
),
rec( TheMatrixStab := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 0 ],[ 0, 1]]
]),
TheRotSubgroup := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 0 ],[ 0, 1]]
]),
BoundaryImage := rec(
ListIFace:=[ 5, 6],
 ListSign := [-1,1],
ListElt := [IdentityMat(2), IdentityMat(2)])
),
rec( TheMatrixStab := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 0 ],[ 0, 1]]
]),
TheRotSubgroup := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 0 ],[ 0, 1]]
]),
BoundaryImage := rec(
ListIFace:=[ 5, 7],
 ListSign := [-1,1],
ListElt := [IdentityMat(2), IdentityMat(2)])
),
rec( TheMatrixStab := Group([
[[ -x - 1, -x + 4 ],[ 1, x]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ -x, -x + 4 ],[ 1, x + 1]]
,
[[ x, x - 4 ],[ -1, -x - 1]]
,
[[ 1, 0 ],[ 0, 1]]
,
[[ x + 1, x - 4 ],[ -1, -x]]
]),
TheRotSubgroup := Group([
[[ -x - 1, -x + 4 ],[ 1, x]]
,
[[ -1, 0 ],[ 0, -1]]
,
[[ -x, -x + 4 ],[ 1, x + 1]]
,
[[ x, x - 4 ],[ -1, -x - 1]]
,
[[ 1, 0 ],[ 0, 1]]
,
[[ x + 1, x - 4 ],[ -1, -x]]
]),
BoundaryImage := rec(
ListIFace:=[ 4, 6],
 ListSign := [-1,1],
ListElt := [[[ -x - 1, -1 ],[ 1, 0]], [[ 3*x - 1, x - 6 ],[ -x - 4, -2*x]]])
),
rec( TheMatrixStab := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 0 ],[ 0, 1]]
]),
TheRotSubgroup := Group([
[[ -1, 0 ],[ 0, -1]]
,
[[ 1, 0 ],[ 0, 1]]
]),
BoundaryImage := rec(
ListIFace:=[ 6, 7],
 ListSign := [-1,1],
ListElt := [IdentityMat(2), IdentityMat(2)])
),
],
[
rec( TheMatrixStab := Group([-IdentityMat(2)]),
TheRotSubgroup := Group([-IdentityMat(2)]),
BoundaryImage := rec(
ListIFace:=[ 
7
,
5
,
11
,
1
,
2
], ListSign := [
1
, 
-1
, 
1
, 
-1
, 
1
 ],
ListElt := [
IdentityMat(2)
, 
IdentityMat(2)
, 
IdentityMat(2)
, 
IdentityMat(2)
, 
IdentityMat(2)
]))
, 
rec( TheMatrixStab := Group([-IdentityMat(2)]),
TheRotSubgroup := Group([-IdentityMat(2)]),
BoundaryImage := rec(
ListIFace:=[ 
10
,
6
,
11
,
3
,
2
], ListSign := [
-1
, 
1
, 
-1
, 
1
, 
-1
 ],
ListElt := [
IdentityMat(2)
, 
IdentityMat(2)
, 
[[ x - 6, -2*x - 5 ],[ -2*x, -x + 4]]
, 
IdentityMat(2)
, 
[[ -1, x ],[ 0, -1]]
]))
, 
rec( TheMatrixStab := Group([-IdentityMat(2)]),
TheRotSubgroup := Group([-IdentityMat(2)]),
BoundaryImage := rec(
ListIFace:=[ 
5
,
6
,
9
,
9
,
4
], ListSign := [
1
, 
-1
, 
1
, 
-1
, 
-1
 ],
ListElt := [
IdentityMat(2)
, 
IdentityMat(2)
, 
[[ x - 6, -2*x - 5 ],[ -2*x, -x + 4]]
, 
IdentityMat(2)
, 
IdentityMat(2)
]))
, 
rec( TheMatrixStab := Group([-IdentityMat(2)]),
TheRotSubgroup := Group([-IdentityMat(2)]),
BoundaryImage := rec(
ListIFace:=[ 
11
,
9
,
8
], ListSign := [
1
, 
-1
, 
1
 ],
ListElt := [
[[ -1, -1 ],[ 1, 0]]
, 
[[ -x - 2, -x + 2 ],[ 2, x]]
, 
IdentityMat(2)
]))
, 
rec( TheMatrixStab := Group([-IdentityMat(2)]),
TheRotSubgroup := Group([-IdentityMat(2)]),
BoundaryImage := rec(
ListIFace:=[ 
11
,
9
,
8
], ListSign := [
-1
, 
1
, 
-1
 ],
ListElt := [
IdentityMat(2)
, 
IdentityMat(2)
, 
IdentityMat(2)
]))
],
];

if IsBound(HAP_GCOMPLEX_SETUP[2]) then
x:=HAP_GCOMPLEX_SETUP[2];
else Unbind(x); fi;

