A linear equation for Minkowski sums of polytopes relatively in general position
Komei Fukuda, Christophe Weibel
TL;DR
This paper investigates Minkowski sums of polytopes in general position, establishing a linear relation for their face vectors and demonstrating how maximum face counts are achieved within this family.
Contribution
It introduces a new linear equation relating f-vectors of Minkowski sums and their summands, specifically for polytopes in general position.
Findings
Maximum face count achieved by polytopes in general position
New linear equation for f-vectors of Minkowski sums
Implications for face enumeration in polytope sums
Abstract
The objective of this paper is to study a special family of Minkowski sums, that is of polytopes relatively in general position. We show that the maximum number of faces in the sum can be attained by this family. We present a new linear equation that is satisfied by f-vectors of the sum and the summands. We study some of the implications of this equation.
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Taxonomy
TopicsPoint processes and geometric inequalities · Computational Geometry and Mesh Generation · Polynomial and algebraic computation