I have never seen a reamer like you described. Although I haven't seen a ton of reamers in my life LOL. But everyone I have used has a square 3/8 of an inch end on it so you can put a square 3/8 of an inch female extension t-handle on there. Did you buy the reamer of rent it? If you rented it I would call the company and ask them what you're supposed to turn it with? Good luck we are enjoying this.
Pictures are always welcome!
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