# 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.

Back to Pairwise Compatibility
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Polyform Compatibility
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Polyform Curiosities

Col. George Sicherman
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