Ice, I just realized I never answered your question: why units of 6 and then units of 10?
Well, at first, the TDF treated the STAG like a light armored vehicle--which it technically is. It was assigned in maniples of 2 vehicles, three maniples per lance (for a total of 6), three lances per company, and three companies per battalion, just like all other Taurian combat vees.
But then, someone had the idea, of training INFANTRY troopers to operate a STAG. TDF Infantry are comprised in two five-man maniples per squad (10-men), with three squads per platoon (30-men). By converting one 30-man platoon in every battalion, the TDF has a very cheap, very effective way of adding force multipliers to a leg unit. Since the infantry are already trained and organized on the 10-30 model, they just gave every trooper a STAG and called it a day. Costs 5.5 million Taurian bulls to outfit a single battalion like this, but it is a very good force multiplier.
Hope that answers!
MA