Tiling a Badge with Separated Copies of Three Pentahexes

Introduction

A polyhex is a plane figure formed by joining equal regular hexagons edge to edge. A pentahex is a polyhex with 5 cells. There are 22 pentahexes, not distinguishing reflections and rotations.

Let a polyhex badge be a polyhex whose cell centers form a convex hexagon whose alternate sides have equal length. Here I study the problem of arranging copies of three given pentahexes to form a badge, without letting two copies of a pentahex touch.

A triangular polyhex is an extreme form of a badge. Many of the solutions below are triangular. See the bottom of the page for non-triangular variants.

Navigation

[3 Tiles] [5 Tiles] [9 Tiles] [11 Tiles] [12 Tiles] [15 Tiles] [18 Tiles] [27 Tiles] [38 Tiles] [Non-Triangular Variants]

3 Tiles

5 Tiles

9 Tiles

11 Tiles

12 Tiles

15 Tiles

18 Tiles

27 Tiles

38 Tiles

Non-Triangular Variants

These are non-triangular badges for some triples of pentahexes whose minimal solution above is a triangular badge.

Last revised 2025-06-12.


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Col. George Sicherman [ HOME | MAIL ]