Make the feet “ribs” protrude into the box, with a 45° rebated channel cut into each side that the side pieces slot into maybe? Have the foot detail just extend under the base to support it. That’s a lot of glue area even if the sides and base are thin, and you’d only lose a small part of the volume to the part protruding into the internal volume
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That's what I'd do. Maybe try for thicker sides so you have a bit more meat for the mitres. Or you could just flatten the corners and butt the edges with glue and tiny dowels.
Just been thinking about this a lot because the feet really bug me somehow. I think it probably is do-able as other people have mentioned, but also, are you sure this is a real box someone made and not AI-generated? I hate to have to ask it, but these days... and man, why don't the feet visibly support the box? I guess it could be inlaid... like I said, I don't think it's impossible. Just odd somehow.
Not a wood worker, but:
- tongue and groove for each side where it meets the center (mitered corners)
- cut a 90 degree angle on the interior of the feet and mount on corner
- Screws for extra support on the feet, placed from inside the box
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