Disjoint axis-parallel segments without a circumscribing polygon

TL;DR

This paper constructs a specific example of 17 disjoint axis-parallel line segments in the plane that cannot be enclosed by any polygon, highlighting limitations in polygonal encodings of such segments.

Contribution

The paper provides the first explicit example of disjoint axis-parallel segments lacking a circumscribing polygon, advancing understanding of geometric configurations.

Findings

17 disjoint axis-parallel segments without a circumscribing polygon

Explicit construction of such segments

Highlights limitations in polygonal encodings

Abstract

We construct a family of 17 disjoint axis-parallel line segments in the plane that do not admit a circumscribing polygon.