Crosspolytope

Prove that the crosspolytope $C_n = \{ x \in \mathbb{R}^n \,:\, \pm x_1 \pm x_2 \cdots \pm x_n \leq 1 \}$ is the projection
of $Q_n := \{ (x,y) \in \mathbb{R}^{2n} \,:\, \sum_{i=1}^n y_i = 1, \,\, -y_i \leq x_i \leq y_i \,\, \forall \,\, i=1,\ldots,n \}$ onto the $x$ coordinates.