Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 152 / 2 / b / i / Solution

The cone $\sigma =\mathrm{Cone}(e_1,e_2,e_3)$ and all its faces form the standard fan of affine three-space, soThe complete target fan has primitive raysand every cone generated by a proper subset of them. This is the two-dimensional simplex fan, hence