Problem with making torus graph in Graph3D by identifying edge of a square graph


Background: I want to imply periodicity along the given edges for a graph. For example in a square lattice with identifying parallel edges, you can construct a torus. consider the following image

enter image description here

So I start with the construction of a square lattice network

nmax = 15;(*Length of lattice*) points = Flatten[Table[{i, j}, {i, -nmax, nmax}, {j, -nmax, nmax}],       1];(*list coordinate of the lattice*) d1 = (Sqrt[2] + 1)/2;(*Max distance to construct linked between coordination of the lattice*) d0 = 1/2;(*Min distance to construct linked between coordination of the lattice*) nn = Nearest[points -> "Index"]; (*function which determine the nearest of a vertex. we can do this*)  (*also by for example DistanceMatrixor or NearestNeighborGraph*) ha = Select[    Flatten[ParallelTable[Module[{pp}, pp = nn[points[[i]], {10, d1}];       Select[{i + 0 pp, pp,            Norm /@ ((points[[pp]]\[Transpose] -                 points[[i]])\[Transpose])}\[Transpose],          d1 > #[[3]] &][[All, {1, 2}]]], {i, 1, Length[points]}],      1], #[[1]] > #[[2]] &]; (*I use select to just consider one linke between two vortex ,*) (*This part is somehow hard to catch at a glince but it did not *) (*change following discussion. Consider this line  as a function*) (*making nearest neighbor links*) Graph3D[ha] 

where gives,

enter image description here

now I am looking to identifying edges. I use the following, for the left and right one

vortexL =points//SortBy[Flatten[Position[#[[All, 1]], Max[#[[All, 1]]]]], points[[#, 2]] &] &; vortexR =points//SortBy[Flatten[Position[#[[All, 1]], Min[#[[All, 1]]]]],points[[#, 2]] &] &; 

and for up and down edge we have

vortexU =points//SortBy[Flatten[Position[#[[All, 2]], Max[#[[All, 2]]]]], points[[#, 1]] &] &; vortexD =points//SortBy[Flatten[Position[#[[All, 2]], Min[#[[All, 2]]]]],points[[#, 1]] &] &; 

now i define identifier as

vchanger = {Table[vortexL[[i]] -> vortexR[[i]], {i, 1, Length@vortexL}],Table[vortexU[[i]]-> vortexD[[i]], {i, 1, Length@vortexU}]}; 

By applying it on ha (the link address) sequentially you can see how periodicity along those edges established,

ha = ha /. vchanger[[1]]; Graph3D[ha] 

enter image description here

and

ha = ha /. vchanger[[2]]; Graph3D[ha] 

where gives,

enter image description here

although it seems torus, by rotation it, you notify two crossings of the links

enter image description here

Question? So I am wondering, I did a mistake to construct the lattice and implication of periodic boundary condition, or this is the problem of Mathematica? Do someone has an option for Graph3D to make it correct shape?

Update My problem is almost the visualization of correct geometry this lattice has.