七十八角形
2 cos  2 π 78 + ω ⋅ 2 cos  46 π 78 + ω 2 ⋅ 2 cos  34 π 78 = − 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 3 2 cos  2 π 78 + ω 2 ⋅ 2 cos  46 π 78 + ω ⋅ 2 cos  34 π 78 = − 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 3 {\displaystyle {\begin{aligned}2\cos {\frac {2\pi }{78}}+\omega \cdot 2\cos {\frac {46\pi }{78}}+\omega ^{2}\cdot 2\cos {\frac {34\pi }{78}}=&{\sqrt[{3}]{\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}}}\\2\cos {\frac {2\pi }{78}}+\omega ^{2}\cdot 2\cos {\frac {46\pi }{78}}+\omega \cdot 2\cos {\frac {34\pi }{78}}=&{\sqrt[{3}]{\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}}}
cos  2 π 78 = 1 6 ( − 1 − 13 + 6 ( 13 + 3 13 ) 4 + − 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 3 + − 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 3 ) {\displaystyle {\begin{aligned}\cos {\frac {2\pi }{78}}=&{\frac {1}{6}}\left({\tfrac {-1-{\sqrt {13}}+{\sqrt {6\left(13+3{\sqrt {13}}\right)}}}{4}}+{\sqrt[{3}]{\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}}}+{\sqrt[{3}]{\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}}}\right)\\\end{aligned}}}