I'll be honest and say I have no clue where the origin of the triangular ground rod configuration came from. I can tell you it really doesn't serve any purpose, at least, not so great that the benefits verses another configuration would ever be noticable or documentable.
I believe the intent is to create ONE large electrode out of three rather crappy individual electrodes. Once the total surface area in contact with the earth + calculating in the "sphere of influence" + the typical longer rods used in this cofiguration = lower earth resistance. (Not that any of that really matters all that much)
I'm sure there is some creative math and physics to the whole idea, but when all is said and done, none of it really matters all the much.
Theoretically, if you want to create a grounding system out of three ground rods which would positively be more effective than any "code permitted" configuration, you could do something like this:
Lay the three ground rods in 24" deep trenches so the middle rod is 180? perpendicular to the service / structure. The other two rods angled somewhere around 45? in realtion to the middle rod. Run a #6 AWG to the middle rod and bond the other two rods.
This would probably give you the best possible grounding configuration for use with a LPS and will be more than sufficient for any other typical service grounding.