Edge connectivity of simplicial polytopes

We show that the graph of a simplicial polytope of dimension $d\ge 3$ has no nontrivial minimum edge cut with fewer than $d(d+1)\mathrm{/}2$ edges, hence the graph is $\min \{\delta ,d(d+1)\mathrm{/}2\}$-edge-connected where $\delta$ denotes the minimum degree. When $d=3$, this implies that every minimum edge cut in a plane triangulation is trivial. When $d\ge 4$, we construct a simplicial $d$-polytope whose graph has a nontrivial minimum edge cut of cardinality $d(d+1)\mathrm{/}2$, proving that the aforementioned result is best possible.