gap> L:=[ [ 1, 4, 5 ], [ 2, 6, 3 ] ];;
gap> M:=[ [ 3, 4, 5 ], [ 6, 1, 2 ] ];;
gap> N:=[ [ 2, 3, 5 ], [ 6, 4, 1 ] ];;
gap> P:=[ [ 1, 2, 5 ], [ 6, 3, 4 ] ];;
gap> Y:=PoincareOctahedronCWComplex(L,M,N,P);;
gap> IsClosedManifold(Y);
true

gap> G:=FundamentalGroup(Y);;
gap> StructureDescription(G);
"SL(2,3)"

gap> R:=ChainComplexOfUniversalCover(Y);
Equivariant chain complex of dimension 3

gap> List([0..3],R!.dimension);
[ 1, 2, 2, 1 ]
