polyDB: A Database for Polytopes and Related Objects
Andreas Paffenholz
TL;DR
polyDB is an accessible database for discrete geometric objects like polytopes and matroids, integrating web and software interfaces to facilitate research and computations in combinatorial and tropical geometry.
Contribution
It introduces the structure and usage of polyDB, a new database that consolidates datasets of polytopes and related objects for geometric research.
Findings
Computed free sums of polytopes in the database
Analyzed skew bipyramids among smooth Fano polytopes in dimension up to 8
Demonstrated the database's utility for geometric computations
Abstract
polyDB is a database for discrete geometric objects. The database is accessible via web and an interface from the software package polymake. It contains various datasets from the area of lattice polytopes, combinatorial polytopes, matroids and tropical geometry. In this short note we introduce the structure of the database and explain its use with a computation of the free sums and certain skew bipyramids among the class of smooth Fano polytopes in dimension up to 8.
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Taxonomy
TopicsPolynomial and algebraic computation · Computational Geometry and Mesh Generation · Commutative Algebra and Its Applications