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I have a unit cube and plane, given by its normal vector and variable d. How can I found d value, so plane-cube intersection produce maximal number of vertices (6, 5 or 4) for given plane normal ?

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Hint:

  • Intersection of two planes is at least a line (and sometimes a plane).
  • To obtain a point you need to intersect your plane with some lines (or points).
  • Perform an orthogonal projection of every edge of the cube onto your normal vector and see what happens (possibly draw a picture).
  • Note that there are many special cases...

I hope this helps $\ddot\smile$

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