$(\mathbb R^2,+)$$\{0\}$$\{mv|m\in \mathbb Z\}$$v$$\mathbb R^2$$\{mv+nw|m,n\in \mathbb Z\}$$v$$w$$\mathbb R^2$$L$$L$$\mathcal C_i$$\mathcal D_i$$i=1,2,3,4,6$$\mathcal C_i$$i$$\mathcal D_i$$i$