File: 12.35.txt

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gap-hap 1.70%2Bds-1
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gap> Y:=PoincareDodecahedronCWComplex(
> [[1,2,3,4,5],[6,7,8,9,10]],
> [[1,11,16,12,2],[19,9,8,18,14]],
> [[2,12,17,13,3],[20,10,9,19,15]],
> [[3,13,18,14,4],[16,6,10,20,11]],
> [[4,14,19,15,5],[17,7,6,16,12]],
> [[5,15,20,11,1],[18,8,7,17,13]]);
Regular CW-complex of dimension 3
gap> IsClosedManifold(Y);
true
gap> List([0..3],n->Homology(Y,n));
[ [ 0 ], [  ], [  ], [ 0 ] ]
gap> StructureDescription(FundamentalGroup(Y));
"SL(2,5)"