kill(all)$

      This problem is not yet solved and the angle relation needs refining.

van=facebook.com/LearningCalculus$

      The interior angles of a polygon must sum to:

totalAngle(n):=(n-2)*%pi$

totalAngle(6);

ourHexagonAngles(x,y,z):=2*(2*%pi/x)+
                         2*(2*%pi/y)+
                         2*(2*%pi/z)+
                         2*(%pi/2-%pi/x)+
                         2*(%pi/2-%pi/y)+
                         2*(%pi/2-%pi/z)
                         =totalAngle(6)$

ourHexagonAngles(x,y,z);

factor(%);

expand(%);

f(x,y,z):=2/x+2/y+2/z=1;

solve(%,(x,y,z));

f(2,1,2);

2*2*%pi/x+u=%pi;

solve(%,u);

expand(%);

factor(%);