I have found an imperfect way to do this, it has some problems but it is a start.
I use the properties of the Dashed Stroke
:
Weight
determines the radius of the dots
Cap
and Corner
are both set to rounded
- The buttons to the right of
Dashed Line
allow the dashes to be aligned to the corers.
- Setting the
dash
length to 0.1pt
makes a dash with rounded ends into a nearly-perfect circle
- If the
gap
length is set to an amount that is longer than any of the line segments, the dashes will only appear on the corners (Because we set them to align with corners)

Then we have a stroke that looks like this:

I use the Appearance
panel to add a new stroke - and change the settings on the new stroke back to your standard settings you were using before.

to achieve a stroke that looks like this:

If this Appearance
is applied to your matrix of triangles (I used a Graphic Style
) it should add dots to all of the corners. You can see some imperfections in my example, but perhaps with some fine tuning they could be minimized.
