Marvelous Slices of Orthogonal Matrices
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).
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Advanced Algebra and Geometry
Polynomial and algebraic computation
Publication details
- Journal / source
- Experimental Mathematics
- Pages
- 1–12
- Publication date
- 7 October 2026
- Language
- EN