$$P:=\{(0,0,0)+\alpha e_1 + \beta e_2 + \gamma e_3 , \alpha + \beta + \gamma \in [0,1]\}\subset A$$
Hey,
I'm having trouble understanding this definition. We are currently doing affine spaces in our lectures and this is one definition for an exercise. The text says that $e_1,e_2,e_3$ and $(0,0,0)$ span a polygon but I don't know how to imagine. When I try to imagine, I think of three vectors coming from $(0,0,0)$ but they would span a something like a cube. Where is my fallacy?
I'm thankful for any kind of help! ;)