七十八角形
( 2 cos  2 π 78 + ω ⋅ 2 cos  46 π 78 + ω 2 ⋅ 2 cos  34 π 78 ) 3 = 3 x 1 + 2 cos  2 π 26 + 2 cos  6 π 26 + 2 cos  18 π 26 + 6 ( x 4 − 2 ) + 3 ω ( 2 x 1 + x 3 + 2 cos  14 π 26 + 2 cos  10 π 26 + 2 cos  22 π 26 ) + 3 ω 2 ( 2 x 1 + x 2 + 2 cos  14 π 26 + 2 cos  10 π 26 + 2 cos  22 π 26 ) = 3 x 1 + 1 + 13 2 + 6 ( x 2 − 2 ) + 3 ω ( 2 x 1 + x 3 + 1 − 13 2 ) + 3 ω 2 ( 2 x 1 + x 2 + 1 − 13 2 ) = − 104 + 34 13 − 3 6 ( 13 + 3 13 ) + 15 6 ( 13 − 3 13 ) − 3 3 ( 2 13 + 6 ( 13 + 3 13 ) − 6 ( 13 − 3 13 ) ) i 8 ( 2 cos  2 π 78 + ω 2 ⋅ 2 cos  46 π 78 + ω ⋅ 2 cos  34 π 78 ) 3 = 3 x 1 + 2 cos  2 π 26 + 2 cos  6 π 26 + 2 cos  18 π 26 + 6 ( x 4 − 2 ) + 3 ω 2 ( 2 x 1 + x 3 + 2 cos  14 π 26 + 2 cos  10 π 26 + 2 cos  22 π 26 ) + 3 ω ( 2 x 1 + x 4 + 2 cos  14 π 26 + 2 cos  10 π 26 + 2 cos  22 π 26 ) = 3 x 1 + 1 + 13 2 + 6 ( x 2 − 2 ) + 3 ω 2 ( 2 x 1 + x 3 + 1 − 13 2 ) + 3 ω ( 2 x 1 + x 2 + 1 − 13 2 ) = − 104 + 34 13 − 3 6 ( 13 + 3 13 ) + 15 6 ( 13 − 3 13 ) + 3 3 ( 2 13 + 6 ( 13 + 3 13 ) − 6 ( 13 − 3 13 ) ) i 8 {\displaystyle {\begin{aligned}\left(2\cos {\frac {2\pi }{78}}+\omega \cdot 2\cos {\frac {46\pi }{78}}+\omega ^{2}\cdot 2\cos {\frac {34\pi }{78}}\right)^{3}=&3x_{1}+2\cos {\frac {2\pi }{26}}+2\cos {\frac {6\pi }{26}}+2\cos {\frac {18\pi }{26}}+6(x_{4}-2)+3\omega \left(2x_{1}+x_{3}+2\cos {\frac {14\pi }{26}}+2\cos {\frac {10\pi }{26}}+2\cos {\frac {22\pi }{26}}\right)+3\omega ^{2}\left(2x_{1}+x_{2}+2\cos {\frac {14\pi }{26}}+2\cos {\frac {10\pi }{26}}+2\cos {\frac {22\pi }{26}}\right)\\=&3x_{1}+{\frac {1+{\sqrt {13}}}{2}}+6(x_{2}-2)+3\omega \left(2x_{1}+x_{3}+{\frac {1-{\sqrt {13}}}{2}}\right)+3\omega ^{2}\left(2x_{1}+x_{2}+{\frac {1-{\sqrt {13}}}{2}}\right)\\=&{\tfrac {-104+34{\sqrt {13}}-3{\sqrt {6\left(13+3{\sqrt {13}}\right)}}+15{\sqrt {6\left(13-3{\sqrt {13}}\right)}}-3{\sqrt {3}}\left(2{\sqrt {13}}+{\sqrt {6\left(13+3{\sqrt {13}}\right)}}-{\sqrt {6\left(13-3{\sqrt {13}}\right)}}\right)i}{8}}\\\left(2\cos {\frac {2\pi }{78}}+\omega ^{2}\cdot 2\cos {\frac {46\pi }{78}}+\omega \cdot 2\cos {\frac {34\pi }{78}}\right)^{3}=&3x_{1}+2\cos {\frac {2\pi }{26}}+2\cos {\frac {6\pi }{26}}+2\cos {\frac {18\pi }{26}}+6(x_{4}-2)+3\omega ^{2}\left(2x_{1}+x_{3}+2\cos {\frac {14\pi }{26}}+2\cos {\frac {10\pi }{26}}+2\cos {\frac {22\pi }{26}}\right)+3\omega \left(2x_{1}+x_{4}+2\cos {\frac {14\pi }{26}}+2\cos {\frac {10\pi }{26}}+2\cos {\frac {22\pi }{26}}\right)\\=&3x_{1}+{\frac {1+{\sqrt {13}}}{2}}+6(x_{2}-2)+3\omega ^{2}\left(2x_{1}+x_{3}+{\frac {1-{\sqrt {13}}}{2}}\right)+3\omega \left(2x_{1}+x_{2}+{\frac {1-{\sqrt {13}}}{2}}\right)\\=&{\tfrac {-104+34{\sqrt {13}}-3{\sqrt {6\left(13+3{\sqrt {13}}\right)}}+15{\sqrt {6\left(13-3{\sqrt {13}}\right)}}+3{\sqrt {3}}\left(2{\sqrt {13}}+{\sqrt {6\left(13+3{\sqrt {13}}\right)}}-{\sqrt {6\left(13-3{\sqrt {13}}\right)}}\right)i}{8}}\\\end{aligned}}}