I'm looking for an example of $n$-dimensional affine space that is isomorphic with $\mathbb{R}^n$ as affine space but not with respect to other properties (for example it has different ordering etc.) Thank you.
EDIT: in practice, I am looking for an affine space that has more or less structure than $\mathbb{R}^n$. Intuitively $\mathbb{R}^n$ has "more structure" than a canonical affine space because, by its field properties, it has a special point (that is the zero with respect to addition). I need an example of affine space different from $\mathbb{R}^n$ but having the same dimension.