Algebraic Degrees of 3-Dimensional Polytopes
Mara Belotti, Michael Joswig, Marta Panizzut
TL;DR
This paper investigates the algebraic degrees of 3-dimensional polytope realizations with edges tangent to the unit sphere, initiating a new research area on constrained realization spaces.
Contribution
It introduces the study of algebraic degrees in constrained polytope realizations, expanding understanding of realization spaces under geometric constraints.
Findings
Analysis of algebraic degrees for 3-polytopes with tangent edges
Connection to classical results by Koebe, Schramm, and Springborn
Foundation for future research on constrained realization spaces
Abstract
Results of Koebe (1936), Schramm (1992), and Springborn (2005) yield realizations of -polytopes with edges tangent to the unit sphere. Here we study the algebraic degrees of such realizations. This initiates the research on constrained realization spaces of polytopes.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Commutative Algebra and Its Applications · Computational Geometry and Mesh Generation