三十八角形
x 1 = 2 cos  2 π 38 + 2 cos  22 π 38 + 2 cos  14 π 38 = 1 + − 133 + 57 3 i 2 3 + − 133 − 57 3 i 2 3 3 x 2 = 2 cos  6 π 38 + 2 cos  10 π 38 + 2 cos  34 π 38 = 1 + ω 2 − 133 + 57 3 i 2 3 + ω − 133 − 57 3 i 2 3 3 x 3 = 2 cos  18 π 38 + 2 cos  30 π 38 + 2 cos  26 π 38 = 1 + ω − 133 + 57 3 i 2 3 + ω 2 − 133 − 57 3 i 2 3 3 {\displaystyle {\begin{aligned}&x_{1}=2\cos {\frac {2\pi }{38}}+2\cos {\frac {22\pi }{38}}+2\cos {\frac {14\pi }{38}}={\frac {1+{\sqrt[{3}]{\frac {-133+57{\sqrt {3}}i}{2}}}+{\sqrt[{3}]{\frac {-133-57{\sqrt {3}}i}{2}}}}{3}}\\&x_{2}=2\cos {\frac {6\pi }{38}}+2\cos {\frac {10\pi }{38}}+2\cos {\frac {34\pi }{38}}={\frac {1+\omega ^{2}{\sqrt[{3}]{\frac {-133+57{\sqrt {3}}i}{2}}}+\omega {\sqrt[{3}]{\frac {-133-57{\sqrt {3}}i}{2}}}}{3}}\\&x_{3}=2\cos {\frac {18\pi }{38}}+2\cos {\frac {30\pi }{38}}+2\cos {\frac {26\pi }{38}}={\frac {1+\omega {\sqrt[{3}]{\frac {-133+57{\sqrt {3}}i}{2}}}+\omega ^{2}{\sqrt[{3}]{\frac {-133-57{\sqrt {3}}i}{2}}}}{3}}\\\end{aligned}}}