How can I improve the quality of shape created by Graphics3D?

Question

I created this shape using Graphics3D and then Export as pdf, but the quality is not homogenous where in some sphere there are black dots. How can I remove that and get a very nice shape? I am using M12.1.1. Win10(64), RAM 8G

ax := 0; az := 2; ay := 0; rs = 0.1; rl = 0.01;
unitCell3D[x_, y_, z_] := {Red, Sphere[{x + ax, y + ay, az}, rs], Red,
   Sphere[{x + ax, y + ay + 2/3 Sin[120 Degree], az}, rs], Black, 
  Cylinder[{{x + ax, y + ay, az}, {x + ax, 
     y + ay + 2/3 Sin[120 Degree], az}}, rl], Black, 
  Cylinder[{{x + ax, y + ay, az}, {x + ax + Cos[30 Degree]/2, 
     y + ay - Sin[30 Degree]/2, az}}, rl], Black, 
  Cylinder[{{x + ax, y + ay, az}, {x + ax - Cos[30 Degree]/2, 
     y + ay - Sin[30 Degree]/2, az}}, rl]}

f2 = Graphics3D[
  Block[{unitVectA = {Cos[120 Degree], Sin[120 Degree], 0}, 
    unitVectB = {1, 0, 0}}, 
   Table[unitCell3D @@ (unitVectA j + unitVectB k), {j, 20}, {k, 
     20}]], PlotRange -> {{-0.1, 10.128}, {1.3, 13.0}, {-0.3, 2.3}}, 
  Boxed -> False, Axes -> False]
ax := 0; az := 0; ay := 0;
unitCell3D[x_, y_, z_] := {Blue, Sphere[{x + ax, y + ay, az}, rs], 
  Blue, Sphere[{x + ax, y + ay + 2/3 Sin[120 Degree], az}, rs], Black,
   Cylinder[{{x + ax, y + ay, az}, {x + ax, 
     y + ay + 2/3 Sin[120 Degree], az}}, rl], Black, 
  Cylinder[{{x + ax, y + ay, az}, {x + ax + Cos[30 Degree]/2, 
     y + ay - Sin[30 Degree]/2, az}}, rl], Black, 
  Cylinder[{{x + ax, y + ay, az}, {x + ax - Cos[30 Degree]/2, 
     y + ay - Sin[30 Degree]/2, az}}, rl]}

f1 = Graphics3D[
  Block[{unitVectA = {Cos[120 Degree], Sin[120 Degree], 0}, 
    unitVectB = {1, 0, 0}}, 
   Table[unitCell3D @@ (unitVectA j + unitVectB k), {j, 20}, {k, 
     20}]], PlotRange -> {{-0.1, 10.128}, {1.3, 13.0}, {-0.3, 1.3}}, 
  Boxed -> False, Axes -> False]   

sheet = Show[f2, f1]
Export["F:\\..path..\\sheet.pdf", sheet, 
 ImageResolution -> 1200]  

Answer 1

Adding EdgeForm[None] just before you start the cylinders seems to do the trick for me and all the black dots have gone. Clearly Mathematica has trouble occluding lines and it's possibly a z-fighting issue. Don't forget to apply this to both sets of cylinders - I've only shown the ones connecting the red spheres below:

ax := 0; az := 2; ay := 0; rs = 0.1; rl = 0.01;
unitCell3D[x_, y_, z_] := {Red, Sphere[{x + ax, y + ay, az}, rs], Red,
   Sphere[{x + ax, y + ay + 2/3 Sin[120 Degree], az}, rs], 
  EdgeForm[None], Black, 
  Cylinder[{{x + ax, y + ay, az}, {x + ax, 
     y + ay + 2/3 Sin[120 Degree], az}}, rl], Black, 
  Cylinder[{{x + ax, y + ay, az}, {x + ax + Cos[30 Degree]/2, 
     y + ay - Sin[30 Degree]/2, az}}, rl], Black, 
  Cylinder[{{x + ax, y + ay, az}, {x + ax - Cos[30 Degree]/2, 
     y + ay - Sin[30 Degree]/2, az}}, rl]}

As @Chip Hurst noted, it happens because by default "EdgeDepthOffset" is True which allows the edges of the cylinders to peek through the faces of the spheres. If you add Method -> {"EdgeDepthOffset" -> False} to each of your Graphics3D commands it also removes the artefacts.