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arXiv · 2510.07244

Geometry of dyadic polygons II: isomorphisms of dyadic triangles

A. Mućka·A. B. Romanowska
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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 $D^2$ of the real plane $R^2$ 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 $D^2$, 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.

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A. Mućka, A. B. Romanowska. 2025-10-08. Geometry of dyadic polygons II: isomorphisms of dyadic triangles. https://arxiv.org/abs/2510.07244

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