#This example uses Polymake.
psi1:= [[1,0,1], [0,-1,0], [0,0,1]];;
psi2:= [[1,0,0], [0,1,1], [0,0,1]];;
G:=AffineCrystGroupOnLeft([psi1,psi2]);;
G:=StandardAffineCrystGroup(G);
Print(G,"\n");
Y:=EquivariantEuclideanSpace(G,[1/3,1/3]);
Print(Y,"\n");
NumbersOfCellOrbits:=List([0..2],Y!.dimension);
Print(NumbersOfCellOrbits,"\n");
VertexStabilizerOrders:= List([1,2],i->Order(Y!.stabilizer(0,i)));
Print(VertexStabilizerOrders,"\n");
EdgeStabilizerOrders:= List([1,2,3],i->Order(Y!.stabilizer(1,i)));
Print(EdgeStabilizerOrders,"\n");
FaceStabilizerOrders:=Order(Y!.stabilizer(2,1));
Print(FaceStabilizerOrders,"\n");
Print(Size(Y!.boundary(2,1)),"\n");
F:=FundamentalGroupOfQuotient(Y);
Print(F,"\n");
Print(RelatorsOfFpGroup(F),"\n");
