An actual literal triangular cross-section would be unpleasant to hold because of the sharp edges, I think. So you need to get rid of those somehow. If planar surfaces are the easiest things to make, then the best you can do is to cut off the corners with straight lines, at which point you have a hexagon.
Not necessarily a regular hexagon, though. You might have long sides alternating with short ones. But a regular-hexagon writing tool behaves sufficiently like a rounded-off-triangular one for many purposes.
And a triangular section stylus would need custom tooling, but a hexagonal section stylus has parallel faces so it can be made with a standard hammer and anvil.
Such a stylus was featured in a short story set in Cicero's time (he even shows up at the end).
[spoilers]
It's "Mightier than the Sword", by John Maddox Roberts, a historical mystery tale. The triangular shape of the criminal's stylus is key, and he's caught when the investigator asks to borrow it:
"Actually, I didn't really forget my own stylus today." I took it out. "You see, the common styli are round or quadrangular. Mine, for instance, is slightly oval in cross-section." Cicero and his friends drew out their own implements and showed them. All were as I had described. Cicero's was made of ivory, with a silver scraper.
(Part of the writer's SPQR series - I find them well researched and not leaking too much of the modern mindset into classical times.)
Not necessarily a regular hexagon, though. You might have long sides alternating with short ones. But a regular-hexagon writing tool behaves sufficiently like a rounded-off-triangular one for many purposes.