How to fit a cuboid into a polyhedra?

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I have multiple points which create a solid (polyhedra). And now I want to place a cuboid inside this solid in a way that it uses the maximum amout of space inside.

Are there any solutions for this problem? Or how to get an idea of the solution?

My problem

I have sketched it in Blender: in black lines you can see the wireframe (connected points) and in orange lines the cube. It is placed inside with maximum volume usage.