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In a regular hexagon (all sides and angles the same), all interior angles are 120 degrees (see Wikipedia). Draw a regular hexagon with a diagonal joining the left corner of the bottom with the opposite corner. Let this diagonal have length two as suggested below. Draw a line from the top end of the diagonal to the other corner of the base below it, forming a right triangle with angles 90,60,60. Call the height of this triangle d. The sine of 60 degrees is equal to d/2. Solving this gives d=sqrt(3). Thus a regular hexagon with a diagonal length of 2 has distance sqrt(3) between opposite sides. It is not possible to have a regular hexagon with diagonal length 2 and height 1.5. The problem below states that the distance between any two opposite corners is 2, the same for all pairs of opposite corners which would make it a regular hexagon. This is an impossibility. No such soccer ball exists! Thx, L. Dame  


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