Compound Perfect Squared Squares of the Order Twenties

TL;DR

This paper discusses the complete enumeration of low-order compound perfect squared squares (CPSSs) with orders ranging from 24 to 29, providing a comprehensive catalog of these geometric dissections.

Contribution

It presents the complete enumeration of low-order CPSSs up to order 29, expanding the known catalog of such dissections and confirming their classifications.

Findings

208 low-order CPSSs in orders 24 to 28

620 CPSSs up to order 29

Complete enumeration of CPSSs in these orders

Abstract

P. J. Federico used the term low-order for perfect squared squares with at most 28 squares in their dissection. In 2010 low-order compound perfect squared squares (CPSSs) were completely enumerated. Up to symmetries of the square and its squared subrectangles there are 208 low-order CPSSs in orders 24 to 28. In 2012 the CPSSs of order 29 were completely enumerated, giving a total of 620 CPSSs up to order 29.