Abstract.
In this paper we show that an affine bijection f : T 1 → T 2 between two polyhedral complexes T 1 ,T 2 , both of which consist of a union of faces of two convex polyhedra P 1 and P 2 , necessarily respects the cell-complex structure of T 1 and T 2 inherited from P 1 and P 2 , respectively, provided f extends to an affine map from P 1 into P 2 . In addition, we present an application of this result within the area of T-theory to obtain a far-reaching generalization of previous results regarding the equivalence of two distinct constructions of the phylogenetic tree associated to ``perfect'' (that is, treelike) distance data.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received September 30, 1999, and in revised form February 25, 2000. Online publication May 15, 2000.
Rights and permissions
About this article
Cite this article
Dress, A., Huber, K. & Moulton, V. Affine Maps That Induce Polyhedral Complex Isomorphisms . Discrete Comput Geom 24, 49–60 (2000). https://doi.org/10.1007/s004540010034
Issue Date:
DOI: https://doi.org/10.1007/s004540010034