Can one hinge allow for a flat 180° without a gap and an offset at 90° (see drawing)

hinges

the closed and open position for a hinge

I cannot visualize how a hinge can have two pieces of wood butted together with no gap and allow one piece to sit inside the other when at 90°

Note that the underside of the wood cannot have any protrusions, so the hinge cannot go there. Also, this is 1/4"|6mm boards, so I'm planning on gluing the hinge to the wood

This feels like a solved problem, but I don't know what to look for

Cheers

UPDATE: I'm going with Jasen's answer: making the planks themselves the hinge

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Best Answer

You could go down to your local woodworking shop and ask for a full overlay hinge for thin materials. They should point you toward a beast like this:

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Looks like this closed:

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Picture courtesy of https://tddhardware.com/