Is it possible for any rotation in $D_n$ to reverse orientation?

Question

Say, $D_4$ has edges:$1234$, then any rotation preserves orientation.

But, is it possible for any iteration of rotation element (say of: $R^i, 0\leq i\leq n$) $(R^i)^k, k\in\mathbb{Z}$ to reverse orientation, as by reflection shown below for $D_n$?

A reflection can reverse orientation; as along y-axis: $$1234 \stackrel{T}{\longrightarrow} 2143$$ While, reflection along x-axis, gives: $$1234 \stackrel{T}{\longrightarrow} 1342$$

Answer 1

No.

All rotations in $D_n$ are powers of a single $2\pi/n$ radian rotation about the origin; and since that rotation is orientation preserving, each of those powers is also orientation preserving.