The split corner of extremizing symmetric decagons
Year: 2026
Type: preprint
Abstract: Let V be the vertex index and W its restriction to origin-centered enclosing quadrilaterals. Let delta be the untranslated linear Banach-Mazur distance excess from the affine-regular hexagon. For origin-symmetric decagons whose normalized gap (W-V)/delta^2 tends to 1/4, two vertices split at scale delta. In anchored coordinates the possible subsequential limits of their normalized separation are exactly g(1, 2+sqrt(2)), with 1 <= g <= sqrt(2). Equivalently for the amplitude, the attainable limits of the shortest gauge edge length divided by delta form [2+sqrt(2), 2+2sqrt(2)]. A deformed decagon family realizes every amplitude by comparison with the global centered minimum. The classification is provisional and conditional on the stated hexagon premises and local comparisons.
Author: Barritz, Robert
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225450171