gap> Y:=ContractedComplex(S);
Regular CW-complex of dimension 2

gap> CriticalCells(Y);
[ [ 2, 1 ], [ 1, 9 ], [ 1, 11 ], [ 0, 22 ] ]
gap> G:=FundamentalGroup(Y);;
gap> AlexanderPolynomial(G);
x_1^2-x_1+1
