Geometric representation of $\mathbb{Z}_n^\times$ .

Question

We can regard $(\mathbb{Z}_n,+)$ as rotation group of polygon. However, is there any geometric representation of \begin{align} \mathbb{Z}_n^\times=\{\overline{a}\in \mathbb{Z}_n\mid {\rm gcd}(a,n)=1\}? \end{align}

Answer 1

The multiplicative group of integers modulo $n$ can be visualized by constructing its cycle graph, see here.