New answers tagged norms
Yes, a classical result says that every 2-dimensional (real) normed space embeds into L^1. Alternatively, if we assume that the unit ball is a $2n$-gon (the general case then follows by approximation), the corresponding space embeds into $\ell_1^n$. The dual picture is maybe even more transparent : any symmetric $2n$-gon is the Minkoswki sum of $n$ ...
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