A12M:=(({{1, 0, (a3/La), 2+((2 a3)/La)}, {0, 1, (b3/La), 2+((2 b3)/La)}, {0, 0, -(1/La), -(2/La)}, {0, 0, (d3/La), ((2 d3)/La)-La}}))

A13M:={{1,a2 /La,0,2+2 a2/ La},{0,-1/La,0,-2/ La},{0,c2 /La,1,2+2 c2 /La},{0,d2 /La,0,-La+2 d2/ La}}

A14M:={{1,(a2/La),a3+((a2 b3)/La),0},{0,-(1/La),-(b3/La),0},{0,(c2/La),((b3 c2)/La)-La,0},{0,(d2/La),d3+((b3 d2)/La),1}}

A23M:=(({{-(1/La), 0, 0, -(2/La)}, {(b1/La), 1, 0, 2+((2 b1)/La)}, {(c1/La), 0, 1, 2+((2 c1)/La)}, {(d1/La), 0, 0, ((2 d1)/La)-La}}))

A24M:=(({{-1/La, 0, -a3/ La, 0}, {b1/ La, 1, b3+a3 b1/ La, 0}, {c1/ La, 0, -La+a3 c1/ La, 0}, {d1/ La, 0, d3+a3 d1/ La, 1}}))

A34M:=(({{-(1/La), -(a2/La), 0, 0}, {(b1/La), ((a2 b1)/La)-La, 0, 0}, {(c1/La), c2+((a2 c1)/La), 1, 0}, {(d1/La), d2+((a2 d1)/La), 0, 1}}))

Simplify[2+2Cos[2Theta]]

tau24:=Cos[2Pi/3]; tau14:=Cos[2 Pi/3]; tau13:=Cos[2Pi/3]; tau34:=Cos[2Pi/3]; tau14:=Cos[2Pi/3]; tau23:=Cos[2 Pi/3];tau12:=Cos[2Pi/3]

Eigenvectors[A12M]

La=1.5; b1=1;c1=1; b3=1; a2=((1+(La^2)+2 La tau34)/b1);c2=((1+(La^2)+2 La tau14)/b3);d2=((1+(La^2)+2 La tau13)/(2 ));d3=(1/2) (1+(La^2)+2 La tau12);a3=((1+(La^2)+2 La tau24)/(c1 ));a2=((1+(La^2)+2 La tau34)/b1);d1=(1/2) (1+(La^2)+2 La tau23)

M12:=A12M; M13:=A13M; M14:=A14M; MI12:=Inverse[A12M];MI13:=Inverse[A13M]; MI14:=Inverse[A14M];

M23:=A23M; M24:=A24M; M34:=A34M; MI23:=Inverse[A23M]; MI24:=Inverse[A24M]; MI34:=Inverse[A34M]

FM[1]:=N[M12];FM[2] := N[M13];FM[3] := N[M14];FM[4] := N[MI12];FM[5]:=N[MI13];FM[6]:=N[MI14];FM[7]:= N[M23];FM[8]:=N[M24];FM[9]:=N[M34];FM[10]:=N[Inverse[M23]];FM[11]:=N[Inverse[M24]];FM[12]:=N[Inverse[M34]]

e1={1,0,0,0}; e2:={0,1,0,0}; e3:={0,0,1,0}; e4:={0,0,0,1}

Array[STE, 4]

STE[1]:=e1; STE[2]:=e2; STE[3]:=e3; STE[4]:=e4

TM:=Transpose[{{3,0,0,0}, {3, 1, 0, 1}, {3, 0, 1, 0}, {3,0,0,1}}]

Ourpoint[i_,j_,k_,l_]:=If[(TM.FM[i].FM[j].FM[k].STE[l])[[1]]>0,Flatten[{((TM.FM[i].FM[j].FM[k].STE[l])[[2]]/(TM.FM[i].FM[j].FM[k].STE[l])[[1]]), ((TM.FM[i].FM[j].FM[k].STE[l])[[3]]/(TM.FM[i].FM[j].FM[k].STE[l])[[1]]),((TM.FM[i].FM[j].FM[k].STE[l])[[4]]/(TM.FM[i].FM[j].FM[k].STE[l])[[1]])}, 1], {0,0,0}]

Graphics3D[Point[Flatten[Table[Ourpoint[i,j,k,l], {i, 1,6}, {j,1,6}, {k, 1,6}, {l, 4} ],3]],Axes-> True]

Graphics3D[{Line[{{0,0,0},{1/3,0,1/3},{0,1/3,0}, {0,0,1/3}}], Line[{{0,1/3,0},{0,0,0},{0,0,1/3},{1/3,0,1/3}}],  Point[Flatten[Table[Ourpoint[i,j,k,l], {i, 1,6}, {j,1,6}, {k, 1,6}, {l, 4} ],3]]},Axes-> True]

Graphics3D[{Line[{{0,0,0},{1/3,0,1/3},{0,1/3,0}, {0,0,1/3}}], Line[{{0,1/3,0},{0,0,0},{0,0,1/3},{1/3,0,1/3}}],  Point[Flatten[Table[Ourpoint[i,j,k,l], {i, 1,12}, {j,1,12}, {k, 1,12}, {l, 4} ],3]]},Axes-> True]

OurpointA[i_,j_,k_,l_]:=Flatten[{((TM.FM[i].FM[j].FM[k].STE[l])[[2]]/(TM.FM[i].FM[j].FM[k].STE[l])[[1]]), ((TM.FM[i].FM[j].FM[k].STE[l])[[3]]/(TM.FM[i].FM[j].FM[k].STE[l])[[1]]),((TM.FM[i].FM[j].FM[k].STE[l])[[4]]/(TM.FM[i].FM[j].FM[k].STE[l])[[1]])}, 1]

OurpointL2[i_,j_,k_,l_, m_]:=If[(TM.FM[i].FM[j].FM[k].FM[l].STE[m])[[1]]>0, Flatten[{((TM.FM[i].FM[j].FM[k].FM[l].STE[m])[[2]]/(TM.FM[i].FM[j].FM[k].FM[l].STE[m])[[1]]), ((TM.FM[i].FM[j].FM[k].FM[l].STE[m])[[3]]/(TM.FM[i].FM[j].FM[k].FM[l].STE[m])[[1]]),((TM.FM[i].FM[j].FM[k].FM[l].STE[m])[[4]]/(TM.FM[i].FM[j].FM[k].FM[l].STE[m])[[1]])}, 1], {0,0,0}]

Vec:={1,1/4, 1/4, 1/4}

Ourpoint2[i_,j_,k_]:=If[(TM.FM[i].FM[j].FM[k].Vec)[[1]]>0,Flatten[{((TM.FM[i].FM[j].FM[k].Vec)[[2]]/(TM.FM[i].FM[j].FM[k].Vec)[[1]]), ((TM.FM[i].FM[j].FM[k].Vec)[[3]]/(TM.FM[i].FM[j].FM[k].Vec)[[1]]),((TM.FM[i].FM[j].FM[k].Vec)[[4]]/(TM.FM[i].FM[j].FM[k].Vec)[[1]])}, 1], {1/4,1/4,1/4}]

Graphics3D[Flatten[Table[{Line[{Ourpoint[i,j,k,1],Ourpoint[i,j,k,2],Ourpoint[i,j,k,3],Ourpoint[i,j,k,4]}], Line[{Ourpoint[i,j,k,1],Ourpoint[i,j,k,3]}], Line[{Ourpoint[i,j,k,2],Ourpoint[i,j,k,4]}],Line[{Ourpoint[i,j,k,1],Ourpoint[i,j,k,4]}]}, {i, 1, 12}, {j,1,12}, {k, 1,12} ],2],Axes-> True]