Clear[lines1];
Do[Clear[j,k];(*n = 4;*) mod[j_] := 1 + Mod[j-1,n];m = 7;
pi = N[2*Pi/n];
h = Sqrt[4*Sin[pi/2]^2+2*Cos[pi/2] - 2];
pts = Table[Chop[{Cos[pi*(j+k/2)],Sin[pi*(j+k/2)],k*h}],
{j,1,n},{k,1,m}];
tri1[j_,k_] := {pts[[j,k]],pts[[mod[j+1],k]],
pts[[j,k+1]],pts[[j,k]]};
tri2[j_,k_] := {pts[[j,k]],pts[[mod[j],k+1]],
pts[[mod[j-1],k+1]],pts[[j,k]]};
lines1[k_] := Table[tri1[j,k],{j,1,n}];
facelist11 = Map[Line,lines1[1]];
facelist12 = Map[Line,lines1[2]];
facelist13 = Map[Line,lines1[3]];
facelist14 = Map[Line,lines1[4]];
facelist15 = Map[Line,lines1[5]];
facelist16 = Map[Line,lines1[6]];
lines2[k_] := Table[tri2[j,k],{j,1,n}];
facelist21 = Map[Line,lines2[1]];
facelist22 = Map[Line,lines2[2]];
facelist23 = Map[Line,lines2[3]];
facelist24 = Map[Line,lines2[4]];
facelist25 = Map[Line,lines2[5]];
facelist26 = Map[Line,lines2[6]];
gra11 = {Graphics3D[{Thickness[.002],facelist11}],
Graphics3D[{Thickness[.002],facelist12}],
Graphics3D[{Thickness[.002],facelist13}],
Graphics3D[{Thickness[.002],facelist14}],
Graphics3D[{Thickness[.002],facelist15}],
Graphics3D[{Thickness[.002],facelist16}]};
gra21 = {Graphics3D[{Thickness[.002],facelist21}],
Graphics3D[{Thickness[.002],facelist22}],
Graphics3D[{Thickness[.002],facelist23}],
Graphics3D[{Thickness[.002],facelist24}],
Graphics3D[{Thickness[.002],facelist25}],
Graphics3D[{Thickness[.002],facelist26}]};
polylist11 = Map[Polygon,lines1[1]];
polylist12 = Map[Polygon,lines1[2]];
polylist13 = Map[Polygon,lines1[3]];
polylist14 = Map[Polygon,lines1[4]];
polylist15 = Map[Polygon,lines1[5]];
polylist16 = Map[Polygon,lines1[6]];
gra12 = {Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist11}],
Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist12}],
Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist13}],
Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist14}],
Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist15}],
Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist16}]};
polylist21 = Map[Polygon,lines2[1]];
polylist22 = Map[Polygon,lines2[2]];
polylist23 = Map[Polygon,lines2[3]];
polylist24 = Map[Polygon,lines2[4]];
polylist25 = Map[Polygon,lines2[5]];
polylist26 = Map[Polygon,lines2[6]];
gra22 = {Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist21}],
Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist22}],
Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist23}],
Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist24}],
Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist25}],
Graphics3D[{EdgeForm[],
GrayLevel[0.9],polylist26}]};

viewpt = {1000, 300, 350};
Show[gra11, gra21, ViewPoint -> viewpt,  PlotRange -> All,
Lighting -> False, Boxed -> False ];
Show[gra11, gra12,gra21, gra22, ViewPoint -> viewpt,  
PlotRange -> All,
Lighting -> False, Boxed -> False ],{n,3,7}];