2013/01/28 by Roland Grinis, Grinis, Roland, Alexander Kasprzyk +1 · 2 citations
Engineering · Mathematics · #52B20 (Primary) #52B55 #52C07 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #graph theory and CDMA systems #math.CO #msc:52B20 #msc:52B55 #msc:52C07
paper · pdf · doi:10.48550/arxiv.1301.6641
28 pages, 2 figures. Includes an appendix describing the Kreuzer-Skarke algorithm
arxiv created 2013/01/28 · openalex publication_date 2013/01/28 · arxiv updated 2013/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe an algorithm for determining whether two convex polytopes P and Q, embedded in a lattice, are isomorphic with respect to a lattice automorphism. We extend this to a method for determining if P and Q are equivalent, i.e. whether there exists an affine lattice automorphism that sends P to Q. Methods for calculating the automorphism group and affine automorphism group of P are also described. An alternative strategy is to determine a normal form such that P and Q are isomorphic if and only if their normal forms are equal. This is the approach adopted by Kreuzer and Skarke in their PALP software. We describe the Kreuzer-Skarke method in detail, and give an improved algorithm when P has many symmetries. Numerous examples, plus two appendices containing detailed pseudo-code, should help with any future reimplementations of these techniques. We conclude by explaining how to define and calculate the normal form of a Laurent polynomial.