十九角形
よって
6 cos  2 π 19 = α + 3 α + 7 β + 12 − 6 ω ( β + 1 ) + 3 ω 2 ( α − 1 ) 3 + 3 α + 7 β + 12 − 6 ω 2 ( β + 1 ) + 3 ω ( α − 1 ) 3 {\displaystyle {\begin{aligned}6\cos {\frac {2\pi }{19}}=&\alpha +{\sqrt[{3}]{3\alpha +7\beta +12-6\omega (\beta +1)+3\omega ^{2}(\alpha -1)}}+{\sqrt[{3}]{3\alpha +7\beta +12-6\omega ^{2}(\beta +1)+3\omega (\alpha -1)}}\\\end{aligned}}}
整理すると