Pentiamond Compatibility

Introduction

A pentiamond is a plane figure made of five equilateral triangles joined edge to edge. There are 4 such figures, not distinguishing reflections and rotations.

The compatibility problem is to find a figure that can be tiled with each of a set of polyforms. Polyomino compatibility has been widely studied since the early 1990s. Polyiamond compatibility was first studied systematically by Margarita Lukjanska and Andris Cibulis, who published a paper about it with Andy Liu in 2005 in the Journal of Recreational Mathematics.

This web page and my other page, Mixed Polyiamond Compatibility, extend and correct the solutions in the JRM article. See also Zucca's Challenge Problem for Polyiamonds.

Solutions

Here are minimal compatibility figures for pairs of pentiamonds. These solutions are not necessarily unique.

Horizontally Symmetric Variant

This variant solution has horizontal mirror symmetry:

Holeless Variant

The minimal solution for the Q and U pentiamonds has a hole. Here is the minimal holeless solution:

Last revised 2022-12-31.

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Col. George Sicherman [ HOME | MAIL ]