plot sqrt(3) (9 sqrt(2r^2-3)-3r^2-1)/4 +3r^2(2arccos(sqrt(3/8)(1+sqrt(2r^2-3))/r) - sin (2arccos(sqrt(3/8)(1+sqrt(2r^2-3))/r)))/2 for r=sqrt(2)..sqrt(6)

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