Polyhex Exclusion

Introduction

In the 1950s, Solomon W. Golomb investigated the question: how few cells can you remove from the plane to exclude the shape of a given polyomino?

Here I investigate into the related question: how few cells can you remove from the plane to exclude the shape of a given polyhex?

The dihex is hard to exclude! You must remove at least 2/3 of the cells:

To exclude the bent trihex you can remove half the cells. If you have a better exclusion, please let me know.

These trihexes and tetrahexes are excluded minimally.

These tetrahex exclusions are minimal:

These are probably minimal:

These pentahex exclusions are probably minimal:

A straight polyhex of odd order n can be excluded with 1/n holes. Here is an example for n=5:

Col. George Sicherman [ HOME | MAIL ]