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  "body": "\n## Statement\n\nLet $n \\geq 3$.\nThe [[dihedral group|0JZ27DMJ5D]] $D_n$ has [[order|0B85S2V2DR]] $2n$.\n\n## Remarks\n\nA symmetry of the regular $n$-gon is determined by the image of one vertex and by whether it keeps or reverses the orientation.\nThere are $n$ choices for the image of the vertex and $2$ choices for the orientation.\nFor example, $D_3$ has order $6$ and $D_4$ has order $8$.\n\n## Explanations\n\n### L1 human\n\nA symmetry can send a fixed vertex to any of the $n$ vertices.\nAfter that, the polygon can be face up or face down.\nSo there are $n \\cdot 2 = 2n$ symmetries.\n",
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