# Vertical I-Pentomino Compatibility

## Introduction

A *pentomino* is a plane figure made of five
squares joined edge to edge.
The **I** pentomino is a pentomino whose cells are all in a row.

The *compatibility problem*
is to find a figure that can be tiled with each of a set of polyforms.
Here I show the smallest known figure that can be tiled with
a given polyomino
and also with the **I** pentomino,
using the **I** pentomino *only* in vertical position.
These minimal solutions are not necessarily
unique.

For compatibility of arbitrary pairs of pentominoes,
see Pentomino Compatibility.

### No Solution

The **X** pentomino is incompatible
with the **I** pentomino, whether or not
the **I** pentomino may be rotated.

### No Solution

These hexominoes have no solution.

### Unsolved

The **T** hexomino has no known solution.

Last revised 2024-05-27.

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Polyform Curiosities

Col. George Sicherman
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