PENTOMINOES - An Introduction

Polyominoes is the general name given to plane shapes made by joining squares together. Note that the squares must be 'properly' joined edge to edge so that they meet at the corners.
Each type of polyomino is named according to how many squares are used to make it. So there are monominoes (1 square only), dominoes (2 squares), triominoes (3 squares), tetrominoes (4 squares), pentominoes (5 squares), hexominoes (6 squares) and so on.
Though the idea of such shapes has been around in Recreational Mathematics since the beginning of the 1900's, it was not until the latter half of the century that they became as popular as they are today.
In 1953 Solomon W Golomb (an American professor) first introduced their names and outlined their possibilities to mathematicians, who seized on them with considerable interest. They were not brought to the notice of the world in general until 1957 when Martin Gardner (in his famous column in the Scientific American) wrote about them, and they have remained a rich source of spatial recreation ever since.
Pentominoes (made from 5 squares) are the type of polyomino most worked with. There are only 12 in the set (because shapes which are identical by roatation or reflection are not counted). This means that they are few enough to be handleable, yet quite enough to provide diversity.

To make a set of Pentomino pieces
Mark out (lightly) a grid of squares on a piece of card.
Squares having an edge length of 1 cm (or half-an-inch or one-and-a-half cm) are a good size to use.
Draw and cut out the shapes show below.
The letters given by each are those used to identify the shapes.
There are many problems and investigations associated with Pentominoes.
Some which are available from this site are -
Space-filling Problems - 1
Space-filling Problems - 2
Tessellating with Pentominoes
The Enclosure Problem
The Duplication Problem
The Triplication Problem
The Matching Problem
Space-filling Problems - 3
Space-filling Problems - 4
Answers are not given to problems, but hints are offered in appropriate places.
Other sources of information -
Polyominoes, puzzles, patterns, problems and packingsSimon W Golomb
Princeton University Books 1994ISBN 0-691-08573-0
This the only complete book on the subject but it contains a very large list of other published sources about Polyominoes and similar sorts of ideas.

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