Regular 3-polytopes of type ,n\

For each integer \( n ≥ 3 \), we construct a self-dual regular 3-polytope \( P \) of type \( \{n, n\} \) with \( 2^n n \) flags, resolving two foundamental open questions on the existence of regular polytopes with certain Schl\"afli types. The automorphism group \( Aut(P) \) is explicitly realized as the semidirect product \( F_2ⁿ⁻¹ D₂ₙ \), where \( D₂ₙ \) is the dihedral group of order \( 2n \), with a complete presentation for \( Aut(P) \) is provided. This advances the systematic construction of regular polytopes with prescribed symmetries.