gap> U:=UniversalCover(W);;
gap> G:=U!.group;;
gap> Wtilde:=EquivariantCWComplexToRegularCWComplex(U,Group(One(G)));
Regular CW-complex of dimension 3

gap> Homology(Wtilde,1);
[  ]
gap> Homology(Wtilde,2);
[  ]
gap> Homology(Wtilde,3);
[ 0 ]

gap> F:=FundamentalGroup(Wtilde);
&lt;fp group on the generators [  ]&gt;
