Question: Slicing 3 dimensional and 4 dimensional cube

So basically I'm trying to slice a tesseract, with a 3D surface but first want to be able to slice a cube, with a 2D plane. so I have a 3D plot of a polygon of a face (of a cube) and I want to find the intersection of that with a plane. intersectplot doesn't seem to be working for me, and I'm unsure of how to represent a finite face of a cube as a plane

 

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