For $X=(x_1,\dots,x_n) \in (R^2)^n$$X=(x_1,\dots,x_n) \in (\mathbb{R}^2)^n$, the generated zonotope (zonogon in 2D) is defined by $ Z(X) := \{|\sum_{k=1}^n \sigma_k z_k| : \sigma_1,\dots,\sigma_n \in [0,1] \}. $$ Z(X) := \{\sum_{k=1}^n \sigma_k x_k : \sigma_1,\dots,\sigma_n \in [0,1] \}. $
Which $X$ generate the regular $2n$-gon inscribed in the unit disk centered at the origin?