Why would you want to use an inverter? That massively complicates things. Also, many electronic loads are not too happy running from inverters. Many will run, but they represent a non-linear load, so your inverter may become unhappy LONG before you reach its "rated" Kva rating. Also, an inverter capable of running an entire house will be $$$. Probably cheaper to get a single phase / split-phase generator. Can you trade the genny you have in towards one that is actually better suited to your situation?
Note: I'm assuming you're in N. America with these following comments;
Just use two of the generator's three legs and its neutral for "single phase" supply. This will work to a point, until the generator gets cranky being unevenly loaded. How many Kva are you talking about here?
If this is a permanent connection, replace the single phase panel (in reality, it's a split-phase panel) with a three phase panel.
If you're concerned about leg-to-leg loads receiving a lower voltage (208v on 3ph VS 240v on split phase) you can change things like heater elements to 208v, or use a buck-boost transformer if you absolutely MUST have 240v.
I deal with these issues all the time in the entertainment industry. Most of our loads are 120v single phase, with some three phase motor loads thrown in for good measure. Selecting the proper generator for the loads I'm driving is the first step in properly spec-ing power distro.
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