Mines running on PoE, with a 5.5mm x 2.5mm power connector, but it's possible that it's a 5.5mm x 2.1mm, as the plug I used was was one of those with springy internal connectors, that work OK on both 5.5mm and 2.1mm and 5.5mm by 2.5mm sockets. The non-spring loaded plugs are pin-size critical, so if it's a 2.1mm pin on the HG612 then it won't make reliable contact with a 2.5mm plug, so it is well worth checking the pin diameter on the HG612 (sadly I can't do this right now, as mine is 16 miles away).
The barrel diameter is definitely be 5.5mm, as the only alternative sizes are much smaller, the tiny 3.5mm or 3.1mm barrel diameter, again with varying pin sizes.