# The polyhedral tree complex

@article{Dougherty2022ThePT, title={The polyhedral tree complex}, author={Michael Dougherty}, journal={Combinatorial Theory}, year={2022} }

. The tree complex is a simplicial complex deﬁned in recent work of Belk, Lanier, Margalit, and Winarski with applications to mapping class groups and complex dynamics. This article introduces a connection between this setting and the convex polytopes known as associahedra and cyclohedra. Speciﬁcally, we describe a characterization of these polytopes using planar em- beddings of trees and show that the tree complex is the barycentric subdivision of a polyhedral cell complex for which the cells…

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