Hexagon inside the cube

 

A plane which passes through the cube’s center produces a cross section in form of a square (the leftmost cube in the illustration). A plane which passes through the three corners of the cube only produces a cross section in form of a regular triangle (the rightmost cube in the illustration).The objective is to find the way how the plane should pass through the cube in order to produce a cross section that is a regular hexagon. If the cube’s side is one unit, what is the side of the hexagon ?


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