RIC describes the reverse of this coin as Sol in the middle of a Roman camp, but I have long been in doubt of that. The problem is that Roman camps seem to always be rectangular or square. I have seen many fanciful alternate ideas of what the reverse might represent, however it definitely has something to do with the army because of the reverse legend (VIRT EXERC) which translates to "Valor of the Army". I would also venture that it might be specific to the army in Thessalonica, as this type was only struck in that city. Constantine was also in residence in the city at the time (he stayed in Thessalonica for almost a year after his victory over Licinius), so that was probably also a reason for the special type, but it seems most definitely to be a type for the military. As to what it actually represents, we may never know. I suspect it might be a depiction of a statue or shrine that was favored by the military, set on some sort of pedestal in Thessalonica.
Constantine I
A.D. 319
18x19mm 2.9gm
CONSTAN-TINVS AVG, laureate and cuirassed bust right.
VIRT EXERC [Valor of the army] Plan of Roman camp, Sol standing in the middle raising right hand, holding globe in left, chlamys across left shoulder.
In exergue dot TS dot delta dot
RIC VII Thessalonica 66
Maybe officina A, if so it is an unlisted officina, but delta can look like an A.