Work

Marvelous Slices of Orthogonal Matrices

Year: 2026

Type: article

Abstract: The space of 4×4 special orthogonal matrices with zeros on the diagonal decomposes into the union of 14 irreducible surfaces whose intersections are beautifully encoded by the cuboctahedron. Using this decomposition, we exhibit a totally real witness set for SO(4). We explain how to obtain a similar decomposition for SO(5), where the 64 components can be grouped to obtain such a correspondence with the face lattice of a 3-polytope. We show that no such pattern exists for SO(6).

Source: Experimental Mathematics

DOI: 10.1080/10586458.2026.2734037

Authors: Taylor Brysiewicz, Fulvio Gesmundo

Institutions: Western University, Centre National de la Recherche Scientifique, Université Toulouse III - Paul Sabatier, Université Fédérale de Toulouse Midi-Pyrénées, Toulouse Mathematics Institute

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Natural Sciences and Engineering Research Council of Canada

Awards: Institute for Computational and Experimental Research in Mathematics, G4998900716, Computational Algorithms in Numerical and Enumerative Geometry