An orientably-regular map $\mathcal{M}$ is a 2-cell embedding of a finite connected graph in a closed orientable surface such that the group ${\mathrm{\text{Aut}}}^{\circ }M$ of orientation-preserving automorphisms of $\mathcal{M}$ acts transitively on the set of arcs. Such a map $\mathcal{M}$ is called a Cayley map for the finite group G if ${\mathrm{\text{Aut}}}^{\circ }\mathcal{M}$ contains a subgroup, which is isomorphic to G and acts regularly on the set of vertices. Conder and Tucker (2014) classified the regular Cayley maps for finite cyclic groups, and obtain two two-parameter families $\mathcal{M}(n,r)$, one for odd n and one for even n, where n is the order of the regular cyclic group and r is a positive integer satisfying certain arithmetical conditions. In this paper, we classify the regular Cayley maps for dihedral groups in the same fashion. Five two-parameter families ${\mathcal{M}}_i(n,r)$, $1\le i\le 5$, are derived, where 2n is the order of the regular dihedral group and r is an integer satisfying certain arithmetical conditions. For each map ${\mathcal{M}}_i(n,r)$, we determine its valence and covalence, and also describe the structure of the group ${\mathrm{\text{Aut}}}^{\circ }{\mathcal{M}}_i(n,r)$. Unlike the approach of Conder and Tucker, which is entirely algebraic, we follow the traditional combinatorial representation of Cayley maps, and use a combination of permutation group theoretical techniques, the method of quotient Cayley maps, and computations with skew morphisms.

定向规则的地图 $\mathcal{中号}$ 是有限连通图在闭合可定向曲面中的2单元嵌入，因此该组 ${\mathrm{\text{ut}}}^{\circ }\mathrm{中号}$ 的方向保持自同构 $\mathcal{中号}$过渡地作用于该组弧。这样的地图$\mathcal{中号}$如果有限组G被称为Cayley映射${\mathrm{\text{ut}}}^{\circ }\mathcal{中号}$包含一个与G同构的子组，该子组定期作用于一组顶点。Conder和Tucker（2014）对有限循环群的常规Cayley映射进行分类，并获得两个两参数族$\mathcal{中号}（ñ，\mathrm{[R}）$，一个代表奇数n，另一个代表偶数n，其中n是规则循环群的阶数，r是满足某些算术条件的正整数。在本文中，我们以相同的方式对二面体组的常规Cayley映射进行分类。五个二参数家庭${\mathcal{中号}}_{\mathrm{一世}}（ñ，\mathrm{[R}）$， $\mathrm{1个}\le \mathrm{一世}\le 5$导出，其中2 n是规则二面体组的阶数，r是满足某些算术条件的整数。对于每张地图${\mathcal{中号}}_{\mathrm{一世}}（ñ，\mathrm{[R}）$，我们确定其价和价，并描述该组的结构 ${\mathrm{\text{ut}}}^{\circ }{\mathcal{中号}}_{\mathrm{一世}}（ñ，\mathrm{[R}）$。与完全代数的Conder和Tucker方法不同，我们遵循Cayley映射的传统组合表示形式，并使用置换组理论技术，商Cayley映射方法以及具有偏态射态的计算的组合。