Since we don't know the material thickness, a 1/8" bit may be a problem. Especially if the stock is 3/4" thick hardwood. Cutting will really have to...
I'd think the smallest reasonably sized router bit to cut any reasonable depth would be 1/4". So you're gonna lose at least that. And things are out...
I spent a day at a maker's workshop learning how to build a hinged-lid box (roughly 9 x 5 x 3.5h) with cherry and mahogany; it was a fun class and I...