Hooking up 50A cord to 120V-30A supply

[NCBBA11043]

OK all of you EE's and EC's . . .
From what I've read online, 50A shore power is actually 120/240V (2 hot, 1 neutral, 1 ground) fed from a 50A 2 pole breaker. So does that mean that the RV power distribution center is also 120/240 4 wire? Voltage between leg A and leg B is 240V, between either leg and neutral is 120V? And a 2-pole breaker as a main? (as you can tell, I haven't gotten the Silverback 33IK yet). For my previous trailer, I installed a power center with a 20A and a 30A RV receptacle. Both were actually on the same circuit, and circuited from a 20A breaker in the house (I used #10 awg for voltage drop).
So now the major question: Is there a adapter/converter that has a 120V 30A RV male plug at one end, and a 120/240 50A RV female receptacle at the other end that feeds power to both legs of the RV power distribution panel? If I need to make one, am I on the right track? The hot from the 120V 30A would have to connect to both hots on the 50A to provide power to all devices.
Hope this makes sense, and thanks for any help!

[Mojojojo]

All the RV stores carry them or can order them also good to carry both with you. That would be from 50-30 and a 30- 120 standard plug, just don't plab on running a lot if your on a standard plug.

[fonzie]

Here you go...

50 Amp 125/250V RV Female to 30 Amp RV Male Pigtail Adapter with Pull Handles - Furrion IP5431R-SB - Electrical Adapters - Camping World