2026/02/02 by Taylor Brysiewicz, Fulvio Gesmundo · 1 voice
Mathematics · #math.AG #math.CO
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).