We can use the sine law to find P1 P2
By the sine law, P1 P2 = sin 15. We can also find P1 P_3 = sin 60, P1 P4 = sin 90, etc.
So (P1 P2)^2 + (P1 P3)^2 + … + (P11 P12)^2 = 12 (sin 15)^2 + 12 (sin 30)^2 + 12 (sin 45)^2 + … + 12 (sin 90)^2 = 42.
A regular dodecahedron P1P2P3⋯P12 is inscribed in a circle with radius 1.
Compute (P1P2)2+(P1P3)2+⋯+(P11P12)2.
(The sum includes all terms of the form (PiPj)2, where 1≤i<j≤12.
My answer see here: https://web2.0calc.com/questions/plshelp#r7