Quiver combinatorics and triangulations of cyclic polytopes

Motivated by higher homological algebra, we associate quivers to triangulations of even-dimensional cyclic polytopes and prove two results showing what information about the triangulation is encoded in quiver. We first show that cut Iyama Oppermann correspond precisely 2d-dimensional without interior (d+1)-simplices. This implies these form a connected subgraph flip graph. Our second result shows how quiver can be used identify mutable internal d-simplices. points towards theory higher-dimensional mutation might look like gives new way understanding flips polytopes.