dihedral group

《代数学引论》 · 第 27 页

这些群通常称为二面体群，用符号 $D_n$ 表示。

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《Abstract Algebra》 · 第 23–24 页 · Section 1.2「Dihedral Groups」

For each $n\in\mathbb Z^+$, $n\ge3$ let $D_{2n}$ be the set of symmetries of a regular $n$-gon, where a symmetry is any rigid motion of the $n$-gon which can be effected by taking a copy of the $n$-gon, moving this copy in any fashion in $3$-space and then placing the copy back on the original $n$-gon so it exactly covers it. […] Now make $D_{2n}$ into a group by defining $st$ for $s,t\in D_{2n}$ to be the symmetry obtained by first applying $t$ then $s$ to the $n$-gon (note that we are viewing symmetries as functions on the $n$-gon, so $st$ is just function composition - read as usual from right to left). […] In the next paragraph we show $|D_{2n}|=2n$ and so $D_{2n}$ is called the dihedral group of order $2n$.