Periodic forest whose largest clearings are of size 3

Abstract

Miller has observed that there are a finite number of periodic forests whose largest clearings are of size 1 or 2, and an infinite number whose largest clearings are of size 4. In this note the basic theory of periodic forests is outlined, and the number of periodic forests whose largest clearings are of size 3 is examined. There are 12 such forests; their corresponding tessellations are sketched.