Polyiamonds Attaining Extremal Topological Properties, Part II

Abstract: In Part II of this work, we construct crystallized polyiamonds with $h$ holes for every $h\ge1$, that is polyiamonds which use the fewest possible tiles necessary to enclose $h$ holes. Furthermore, we prove that crystallized polyiamonds satisfy a set of structural conditions, and for every $h\ge 3$ there are multiple distinct crystallized polyiamonds with $h$ holes.