Hexagon Inside the Cube
after Martin Gardner
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?