Decompositions of a polygon into centrally symmetric pieces

TL;DR

This paper investigates how to decompose centrally symmetric convex polygons into smaller symmetric convex pieces, establishing bounds on the number of such decompositions and characterizing them specifically for octagons.

Contribution

It provides an upper bound on the number of edge-to-edge, irreducible decompositions of centrally symmetric convex polygons and characterizes these decompositions for octagons.

Findings

Established an upper bound on the number of decompositions for any 2k-gon.

Characterized all such decompositions for octagons.

Contributed to understanding symmetric polygon decompositions.

Abstract

In this paper we deal with edge-to-edge, irreducible decompositions of a centrally symmetric convex $(2k)$-gon into centrally symmetric convex pieces. We prove an upper bound on the number of these decompositions for any value of $k$, and characterize them for octagons.