I like to keep things simple, so I'll skip the letter labels, but include the lines overhanging from the grid:

m = 30 (* number of mesh lines *); h = 2 (* overhang *);
lins = Join[#, Map[Reverse, #, {2}]] & @
       Outer[{##} &, ArrayPad[Range[-1, 1, 2/m], h, "Extrapolated"], {-1, 1}];

Table[Graphics[{AbsoluteThickness[1/100], 
                Table[Line[Map[RotationTransform[θ], lins, {2}]],
                      {θ, 0, π/2 - π/(2 n), π/(2 n)}]}], {n, 3, 6}] // GraphicsRow

(click on the picture to see it in its full resolution splendor)

The original picture had more random orientations for grids B and C. I tried using Manipulate[] to attempt to determine those rotations, but I was not successful. Maybe somebody else can try.

I like to keep things simple, so I'll skip the letter labels, but include the lines overhanging from the grid:

m = 30 (* number of mesh lines *); h = 2 (* overhang *);
lins = Join[#, Map[Reverse, #, {2}]] & @
       Outer[{##} &, ArrayPad[Range[-1, 1, 2/m], h, "Extrapolated"], {-1, 1}];

Table[Graphics[{AbsoluteThickness[1/100], 
                Table[Line[Map[RotationTransform[θ], lins, {2}]],
                      {θ, 0, π/2 - π/(2 n), π/(2 n)}]}], {n, 3, 6}] // GraphicsRow

(click on the picture to see it in its full resolution splendor)

The original picture had more random orientations for grids B and C. I tried using Manipulate[] to attempt to determine those rotations, but I was not successful. If you want to play around with it yourself, have at it:

DynamicModule[{θl = {0, 0, 0}}, 
              Panel[Row[{Dynamic[
                    Graphics[{AbsoluteThickness[1/100], 
                              Table[Line[Map[RotationTransform[θ], lins, {2}]],
                                    {θ, θl}]}, ImageSize -> Medium, 
                             PlotRange -> {{-3/2, 3/2}, {-3/2, 3/2}}]], 
                    Column[Table[With[{i = i}, 
                    Experimental`AngularSlider[Dynamic[θl[[i]]]]], {i, Length[θl]}]]}]]]