Recall the definition of a fan: Let $U$ be a finite dimensional real vector space. Then a fan is a collection $\mathcal{F}$ of cones in $U$ such that (1) If $\sigma \in \mathcal{F …

Is the following conjecture true? Conjecture: Let $M_1$ be a red map and let $M_2$ be a blue map drawn in general position on $S^n$, and let $M$ be their common refinement. There …