gap> for i in [1..25] do
> p:=Manifolds[i]!.cubeFacePairings;
> Print("Manifold ",i," has face pairings:\n");
> Print(p[1],"\n",p[2],"\n",p[3],"\n");
> Print("Fundamental group is: ");
> if i in [ 1, 9, 12, 14, 15, 16, 17, 18, 19, 20, 22, 23, 25 ] then
> Print(StructureDescription(FundamentalGroup(Manifolds[i])),"\n");
> else Print("infinite non-cyclic\n"); fi;
> if Homology(Manifolds[i],3)=[0] then Print("Orientable, ");
> else Print("Non orientable, "); fi;
> Print(ManifoldType(Manifolds[i]),"\n");
> for x in Manifolds[i]!.edgeDegrees do
> Print(x[2]," edges of \"degree\" ",x[1],", ");
> od;
> Print("\n\n");
> od;
Manifold 1 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 7, 8, 4 ] ]
[ [ 1, 2, 3, 4 ], [ 5, 8, 7, 6 ] ]
[ [ 1, 4, 8, 5 ], [ 3, 2, 6, 7 ] ]
Fundamental group is: Z x C2
Non orientable, other
4 edges of "degree" 2, 4 edges of "degree" 4,
Manifold 2 has face pairings:
[ [ 1, 5, 6, 2 ], [ 7, 8, 4, 3 ] ]
[ [ 1, 2, 3, 4 ], [ 1, 5, 8, 4 ] ]
[ [ 5, 8, 7, 6 ], [ 7, 6, 2, 3 ] ]
Fundamental group is: infinite non-cyclic
Non orientable, other
2 edges of "degree" 1, 2 edges of "degree" 3, 2 edges of "degree" 8,
Manifold 3 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 7, 8, 4 ] ]
[ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ] ]
[ [ 1, 4, 8, 5 ], [ 2, 3, 7, 6 ] ]
Fundamental group is: infinite non-cyclic
Non orientable, euclidean
6 edges of "degree" 4,
Manifold 4 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 7, 8, 4 ] ]
[ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ] ]
[ [ 1, 4, 8, 5 ], [ 6, 7, 3, 2 ] ]
Fundamental group is: infinite non-cyclic
Non orientable, euclidean
6 edges of "degree" 4,
Manifold 5 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 7, 8, 4 ] ]
[ [ 1, 2, 3, 4 ], [ 6, 5, 8, 7 ] ]
[ [ 1, 4, 8, 5 ], [ 2, 6, 7, 3 ] ]
Fundamental group is: infinite non-cyclic
Non orientable, euclidean
6 edges of "degree" 4,
Manifold 6 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 4, 8, 7 ] ]
[ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ] ]
[ [ 1, 4, 8, 5 ], [ 2, 3, 7, 6 ] ]
Fundamental group is: infinite non-cyclic
Orientable, euclidean
6 edges of "degree" 4,
Manifold 7 has face pairings:
[ [ 1, 5, 6, 2 ], [ 7, 3, 4, 8 ] ]
[ [ 1, 2, 3, 4 ], [ 1, 5, 8, 4 ] ]
[ [ 5, 8, 7, 6 ], [ 7, 6, 2, 3 ] ]
Fundamental group is: infinite non-cyclic
Orientable, other
2 edges of "degree" 1, 2 edges of "degree" 3, 2 edges of "degree" 8,
Manifold 8 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 4, 8, 7 ] ]
[ [ 1, 2, 3, 4 ], [ 7, 8, 5, 6 ] ]
[ [ 1, 4, 8, 5 ], [ 7, 6, 2, 3 ] ]
Fundamental group is: infinite non-cyclic
Orientable, other
4 edges of "degree" 2, 2 edges of "degree" 8,
Manifold 9 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 4, 8, 7 ] ]
[ [ 1, 2, 3, 4 ], [ 8, 5, 6, 7 ] ]
[ [ 1, 4, 8, 5 ], [ 6, 2, 3, 7 ] ]
Fundamental group is: Q8
Orientable, spherical
8 edges of "degree" 3,
Manifold 10 has face pairings:
[ [ 1, 5, 6, 2 ], [ 4, 8, 7, 3 ] ]
[ [ 1, 2, 3, 4 ], [ 7, 8, 5, 6 ] ]
[ [ 1, 4, 8, 5 ], [ 7, 6, 2, 3 ] ]
Fundamental group is: infinite non-cyclic
Orientable, other
4 edges of "degree" 2, 4 edges of "degree" 4,
Manifold 11 has face pairings:
[ [ 1, 5, 6, 2 ], [ 4, 3, 7, 8 ] ]
[ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ] ]
[ [ 1, 4, 8, 5 ], [ 2, 3, 7, 6 ] ]
Fundamental group is: infinite non-cyclic
Non orientable, euclidean
6 edges of "degree" 4,
Manifold 12 has face pairings:
[ [ 1, 5, 6, 2 ], [ 4, 8, 7, 3 ] ]
[ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ] ]
[ [ 1, 4, 8, 5 ], [ 2, 3, 7, 6 ] ]
Fundamental group is: Z x Z x Z
Orientable, euclidean
6 edges of "degree" 4,
Manifold 13 has face pairings:
[ [ 1, 5, 6, 2 ], [ 4, 8, 7, 3 ] ]
[ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ] ]
[ [ 1, 4, 8, 5 ], [ 7, 6, 2, 3 ] ]
Fundamental group is: infinite non-cyclic
Orientable, euclidean
6 edges of "degree" 4,
Manifold 14 has face pairings:
[ [ 1, 5, 6, 2 ], [ 7, 3, 4, 8 ] ]
[ [ 1, 2, 3, 4 ], [ 7, 8, 5, 6 ] ]
[ [ 1, 4, 8, 5 ], [ 7, 6, 2, 3 ] ]
Fundamental group is: C2
Orientable, spherical
12 edges of "degree" 2,
Manifold 15 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 7, 8, 4 ] ]
[ [ 1, 2, 3, 4 ], [ 1, 5, 8, 4 ] ]
[ [ 5, 8, 7, 6 ], [ 2, 3, 7, 6 ] ]
Fundamental group is: Z
Non orientable, other
4 edges of "degree" 1, 2 edges of "degree" 2, 2 edges of "degree" 8,
Manifold 16 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 4, 8, 7 ] ]
[ [ 1, 2, 3, 4 ], [ 1, 5, 8, 4 ] ]
[ [ 5, 8, 7, 6 ], [ 2, 3, 7, 6 ] ]
Fundamental group is: Z
Orientable, other
4 edges of "degree" 1, 2 edges of "degree" 2, 2 edges of "degree" 8,
Manifold 17 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 4, 8, 7 ] ]
[ [ 1, 2, 3, 4 ], [ 1, 5, 8, 4 ] ]
[ [ 5, 8, 7, 6 ], [ 3, 7, 6, 2 ] ]
Fundamental group is: C4
Orientable, spherical
2 edges of "degree" 1, 2 edges of "degree" 3, 2 edges of "degree" 8,
Manifold 18 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 4, 8, 7 ] ]
[ [ 1, 2, 3, 4 ], [ 8, 4, 1, 5 ] ]
[ [ 5, 8, 7, 6 ], [ 6, 2, 3, 7 ] ]
Fundamental group is: C3 : C4
Orientable, spherical
2 edges of "degree" 2, 4 edges of "degree" 5,
Manifold 19 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 4, 8, 7 ] ]
[ [ 1, 2, 3, 4 ], [ 8, 4, 1, 5 ] ]
[ [ 5, 8, 7, 6 ], [ 3, 7, 6, 2 ] ]
Fundamental group is: C12
Orientable, spherical
2 edges of "degree" 2, 2 edges of "degree" 3, 2 edges of "degree" 7,
Manifold 20 has face pairings:
[ [ 1, 5, 6, 2 ], [ 3, 4, 8, 7 ] ]
[ [ 1, 2, 3, 4 ], [ 5, 8, 4, 1 ] ]
[ [ 5, 8, 7, 6 ], [ 3, 7, 6, 2 ] ]
Fundamental group is: C8
Orientable, spherical
8 edges of "degree" 3,
Manifold 21 has face pairings:
[ [ 1, 5, 6, 2 ], [ 7, 3, 4, 8 ] ]
[ [ 1, 2, 3, 4 ], [ 8, 4, 1, 5 ] ]
[ [ 5, 8, 7, 6 ], [ 7, 6, 2, 3 ] ]
Fundamental group is: infinite non-cyclic
Orientable, euclidean
6 edges of "degree" 4,
Manifold 22 has face pairings:
[ [ 1, 5, 6, 2 ], [ 5, 6, 7, 8 ] ]
[ [ 3, 7, 8, 4 ], [ 7, 6, 2, 3 ] ]
[ [ 1, 2, 3, 4 ], [ 8, 4, 1, 5 ] ]
Fundamental group is: C14
Orientable, spherical
2 edges of "degree" 2, 4 edges of "degree" 5,
Manifold 23 has face pairings:
[ [ 1, 5, 6, 2 ], [ 5, 6, 7, 8 ] ]
[ [ 3, 7, 8, 4 ], [ 7, 6, 2, 3 ] ]
[ [ 1, 2, 3, 4 ], [ 5, 8, 4, 1 ] ]
Fundamental group is: C6
Orientable, spherical
6 edges of "degree" 2, 2 edges of "degree" 6,
Manifold 24 has face pairings:
[ [ 1, 5, 6, 2 ], [ 7, 8, 5, 6 ] ]
[ [ 3, 7, 8, 4 ], [ 2, 3, 7, 6 ] ]
[ [ 1, 2, 3, 4 ], [ 4, 1, 5, 8 ] ]
Fundamental group is: infinite non-cyclic
Orientable, euclidean
6 edges of "degree" 4,
Manifold 25 has face pairings:
[ [ 1, 5, 6, 2 ], [ 6, 7, 8, 5 ] ]
[ [ 3, 7, 8, 4 ], [ 3, 7, 6, 2 ] ]
[ [ 1, 2, 3, 4 ], [ 1, 5, 8, 4 ] ]
Fundamental group is: 1
Orientable, spherical
4 edges of "degree" 1, 4 edges of "degree" 5,
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