Isometry Classes of Planes in $({\mathbb{R}}^3,d_{\mathrm{\infty }})$

We determine geodesics in ${\mathbb{R}}_{\mathrm{\infty }}^n$ (i.e. $($\mathbb{R}$^n, d_{\infty})$)andbyusingthis,classifyplanesuptoisometryin$$\mathbb{R}$_{\infty}^3$.