English

Geometry of dyadic polygons II: isomorphisms of dyadic triangles

Combinatorics 2025-10-09 v1

Abstract

This paper is the second part of a two-part paper investigating the structure and properties of dyadic polygons. A dyadic polygon is the intersection of the dyadic subplane D2D^2 of the real plane R2R^2 and a real convex polygon with vertices in the dyadic plane. Such polygons are described as subreducts (subalgebras of reducts) of the affine dyadic plane D2D^2, or equivalently as commutative, entropic and idempotent groupoids under the binary operation of arithmetic mean. The first part of the paper contained a new classification of dyadic triangles, considered as such groupoids, and a characterization of dyadic triangles with a pointed vertex. This second part investigates isomorphisms of dyadic triangles, and provides a full classification of their isomorphism types.

Keywords

Cite

@article{arxiv.2510.07244,
  title  = {Geometry of dyadic polygons II: isomorphisms of dyadic triangles},
  author = {A. Mućka and A. B. Romanowska},
  journal= {arXiv preprint arXiv:2510.07244},
  year   = {2025}
}