I'm not 100% sure, but I believe we've been told somewhere that the Republic of the Sphere uses 3-squad platoons.
Well TRO 3085 mentions that a Maxim II, a Trajan and two Giggins can lift a full company, which is at most 40 troopers ( the maxim carry's 16, the other three carry 8 each), the Maxims entry mentions that it's standard practices to carry a full platoon.
This would indicate that a platoon is 12 each, and a company is 36 troopers, this would be the same org as the Kuritans.
However the 3085 Supplemental says that the Zugvogel got a configuration to carry a full RAF BA company, This would be the E config, it has a 48 ton bay (effectively 48 troopers), and that the Trireme which is equipped to carry 36 troopers it self carry's only two platoons, this indicates that a RAF platoon is 16 troopers, also the CS config of the Trireme is stated to carry a full platoon which per the RS entry would be 16 troopers, as for an RAF battalion four regular Triremes can carry a full battalion which would be 144 troopers (4x36 = 144, also 3x48 which matchs the company strengths).
The reference (Trajan entry) of a Maxim II, Trajan and 2x Giggins lifting a company would likely have to be a typo for 2x maxims and one each of the other types.
As such per the 3085 Supplemental a RAF Battle Armor Battalion would be
Squad 4x troopers
Platoon 4x Squads (16)
Company 3x Platoons (48)
Battalion 3x Companys (144)
Going off the typical Regiment = 3 battalions an RAF BA Regiment would have 432 troopers, if it uses 4 battalions that would be 576 troopers.