<p>I'm relatively new to 3d printing, and wanted to get a few things understood.
Firstly, I am unclear on how Hexagonal infill is stronger than, say, diamond pattern. </p>

<p>Can anyone explain how the different shape causes the structure to be stronger? I saw a few places that hex is stronger; usually, more vertices means 'weaker' shape (i.e. a triangle is stronger than a square), so how does that work with hex vs diamond?</p>

<p>Also, in small objects, where the printer makes only a single dot as the infill (a dot instead of a line in larger objects), does the infill strengthen the object at all?</p>

<p>EDIT: I am trying to understand the effect of the infill pattern on the <em>strength</em> of the print, regardless of print time.</p>

Correction: I believe I found what you are looking for:
Report from EngineerDog.com
The author concludes that rectilinear infill with a zero degree offset is the strongest. However, I have not seen consensus for or against a certain pattern being strongest. I recommend more investigation .
My original answer:
I don't know that one pattern is significantly stronger than another,
  provided they each bond well with other infill deposits as well as the
  perimeters.
There are studies around. In 3D printing, strength is rarely the only
  consideration; one must optimize for strength
where needed
versus
  time to print.
See
this
as an example of a report which supports the hexagonal or honeycomb
  pattern as the optimal balance between strength and print time.
This
  one
is
  more detailed, but only compares linear infill patterns of varying
  layer thickness and density. There are many such articles, some more
  scientifically conducted than others, available with a simple search.