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Solution to Puzzle 83.  HEXAGON FROM CUBE

How would you cut a plane through a cube, such that its intersection with the cube would be a regular hexagon? 



Let the cube be centered at the origin of a cartesian coordinate system, and the length of each side be 2 units.  Cut the plane so that it passes thru the following points on the edges of the cube:

(1, 0, -1), (0, 1, -1),(1,-1,0),(0,-1,1),(-1,1,0),(-1,0,1)

The points above represents the vertices of the regular hexagon.  These points are at the midpoints of their corresponding edges.  The center of the regular hexagon coincides with the center of the square at the origin.  The sides of the hexagon are on the faces of the cube.   

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The Last Recreations:  Hydras, Eggs, and Other Mathematical Mystifications

Author:  Martin Gardner



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