Regular 3-polytopes of type $\{n,n\}$

For each integer $n\ge 3$, we construct a self-dual regular 3-polytope $\mathcal{P}$ of type $\{n,n\}$ with $2^{n}n$ flags, resolving two foundamental open questions on the existence of regular polytopes with certain Schläfli types. The automorphism group $\mathrm{Aut}(\mathcal{P})$ is explicitly realized as the semidirect product ${\mathbb{F}}_2^{n-1}⋊D_{2n}$, where $D_{2n}$ is the dihedral group of order $2n$, with a complete presentation for $\mathrm{Aut}(\mathcal{P})$ is provided. This advances the systematic construction of regular polytopes with prescribed symmetries.