三十五角形
( 2 cos  2 π 35 + ω ⋅ 2 cos  32 π 35 + ω 2 ⋅ 2 cos  22 π 35 ) 3 = 3 x 1 + x 2 + 6 x 3 + 12 cos  2 π 5 + 3 ω ( 2 x 1 + x 4 + 6 cos  4 π 5 ) + 3 ω 2 ( 2 x 1 + x 2 + x 3 ) = − 2 + 20 5 + 3 14 ( 5 − 5 ) + 14 ( 5 + 5 ) + 3 ω ( − 3 − 5 5 − 2 14 ( 5 − 5 ) − 14 ( 5 + 5 ) ) + 3 ω 2 ( 4 + 2 5 − 14 ( 5 − 5 ) + 14 ( 5 + 5 ) ) 4 = − 7 + 49 5 + 15 14 ( 5 − 5 ) + 2 14 ( 5 + 5 ) − 3 3 ( 7 + 7 5 + 14 ( 5 − 5 ) + 2 14 ( 5 + 5 ) ) i 8 ( 2 cos  2 π 35 + ω 2 ⋅ 2 cos  32 π 35 + ω ⋅ 2 cos  22 π 35 ) 3 = 3 x 1 + x 2 + 6 x 3 + 12 cos  2 π 5 + 3 ω 2 ( 2 x 1 + x 4 + 6 cos  4 π 5 ) + 3 ω ( 2 x 1 + x 2 + x 3 ) = − 2 + 20 5 + 3 14 ( 5 − 5 ) + 14 ( 5 + 5 ) + 3 ω 2 ( − 3 − 5 5 − 2 14 ( 5 − 5 ) − 14 ( 5 + 5 ) ) + 3 ω ( 4 + 2 5 − 14 ( 5 − 5 ) + 14 ( 5 + 5 ) ) 4 = − 7 + 49 5 + 15 14 ( 5 − 5 ) + 2 14 ( 5 + 5 ) + 3 3 ( 7 + 7 5 + 14 ( 5 − 5 ) + 2 14 ( 5 + 5 ) ) i 8 {\displaystyle {\begin{aligned}\left(2\cos {\frac {2\pi }{35}}+\omega \cdot 2\cos {\frac {32\pi }{35}}+\omega ^{2}\cdot 2\cos {\frac {22\pi }{35}}\right)^{3}=&3x_{1}+x_{2}+6x_{3}+12\cos {\frac {2\pi }{5}}+3\omega (2x_{1}+x_{4}+6\cos {\frac {4\pi }{5}})+3\omega ^{2}(2x_{1}+x_{2}+x_{3})\\=&{\tfrac {{-2+20{\sqrt {5}}+3{\sqrt {14\left(5-{\sqrt {5}}\right)}}+{\sqrt {14\left(5+{\sqrt {5}}\right)}}}+3\omega \left(-3-5{\sqrt {5}}-2{\sqrt {14\left(5-{\sqrt {5}}\right)}}-{\sqrt {14\left(5+{\sqrt {5}}\right)}}\right)+3\omega ^{2}\left(4+2{\sqrt {5}}-{\sqrt {14\left(5-{\sqrt {5}}\right)}}+{\sqrt {14\left(5+{\sqrt {5}}\right)}}\right)}{4}}\\=&{\tfrac {{-7+49{\sqrt {5}}+15{\sqrt {14\left(5-{\sqrt {5}}\right)}}+2{\sqrt {14\left(5+{\sqrt {5}}\right)}}}-3{\sqrt {3}}\left(7+7{\sqrt {5}}+{\sqrt {14\left(5-{\sqrt {5}}\right)}}+2{\sqrt {14\left(5+{\sqrt {5}}\right)}}\right)i}{8}}\\\left(2\cos {\frac {2\pi }{35}}+\omega ^{2}\cdot 2\cos {\frac {32\pi }{35}}+\omega \cdot 2\cos {\frac {22\pi }{35}}\right)^{3}=&3x_{1}+x_{2}+6x_{3}+12\cos {\frac {2\pi }{5}}+3\omega ^{2}(2x_{1}+x_{4}+6\cos {\frac {4\pi }{5}})+3\omega (2x_{1}+x_{2}+x_{3})\\=&{\tfrac {{-2+20{\sqrt {5}}+3{\sqrt {14\left(5-{\sqrt {5}}\right)}}+{\sqrt {14\left(5+{\sqrt {5}}\right)}}}+3\omega ^{2}\left(-3-5{\sqrt {5}}-2{\sqrt {14\left(5-{\sqrt {5}}\right)}}-{\sqrt {14\left(5+{\sqrt {5}}\right)}}\right)+3\omega \left(4+2{\sqrt {5}}-{\sqrt {14\left(5-{\sqrt {5}}\right)}}+{\sqrt {14\left(5+{\sqrt {5}}\right)}}\right)}{4}}\\=&{\tfrac {{-7+49{\sqrt {5}}+15{\sqrt {14\left(5-{\sqrt {5}}\right)}}+2{\sqrt {14\left(5+{\sqrt {5}}\right)}}}+3{\sqrt {3}}\left(7+7{\sqrt {5}}+{\sqrt {14\left(5-{\sqrt {5}}\right)}}+2{\sqrt {14\left(5+{\sqrt {5}}\right)}}\right)i}{8}}\\\end{aligned}}}