On the perimeter, diameter and circumradius of ordinary hyperbolic reduced polygons

TL;DR

This paper investigates properties of ordinary reduced polygons in hyperbolic geometry, focusing on perimeter, diameter, and circumradius, and extends known Euclidean results to the hyperbolic setting.

Contribution

It provides new insights into hyperbolic reduced polygons, answering Lassak's questions and extending Euclidean results to hyperbolic geometry.

Findings

Characterization of perimeter, diameter, and circumradius of hyperbolic reduced polygons

Answers to Lassak's questions about hyperbolic reduced polygons

Extension of Fabińska's Euclidean results to hyperbolic geometry

Abstract

A convex body $R$ in the hyperbolic plane is reduced if any convex body $K\subset R$ has a smaller minimal width than $R$. We answer a few of Lassak's questions about ordinary reduced polygons regarding its perimeter, diameter and circumradius, and we also obtain a hyperbolic extension of a result of Fabi\'nska.