Pentominoes

This section assumes you are very familiar with the concepts, terms and ideas for protograf as presented in the Basic Concepts , that you understand all of the Additional Concepts and that you’ve created some basic scripts of your own using the Core Shapes. You also be familiar with the various types of shape’s properties described in the Customised Shapes

Overview

Pentominoes are one of the most popular and well-known types of Polyominoes and each one is composed of 5 squares in one of 12 unique patterns.

They can referred to by their shortcut letter property which has been assigned to each of the 12 shapes, based on their similarity to letters in the Roman alphabet.

Properties

Pentominoes share all the properties of Polyominoes but, instead of a pattern they are defined using a letter.

A letter in uppercase format draws a tetromino in such a way that it resembles that letter; whereas a lowercase letter draws the same basic shape but inverted from left to right.

Examples

The examples below shows how letters are used create a Pentomino or a set of Pentominoes.

Pentomino: Uppercase Letter

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This example shows Pentominoes constructed using commands like:

basics = Common(
    side=0.5,
    outline_stroke="black", outline_width=1)

Pentomino(
    x=2, y=2.5,
    letter="F",
    label="F",
    common=basics)

Each of the twelve shapes is constructed in the same way — setting the letter property to one of: F, I, L, N, P, T, U, V, W, X, Y and Z.

Pentomino: Lowercase Letter

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This example shows Pentominoes constructed using commands like:

basics = Common(
    side=0.5,
    outline_stroke="black", outline_width=1)

Pentomino(
    x=2.5, y=2.5,
    letter="f",
    label="f",
    common=tbasics)

Each of the twelve shapes is constructed in the same way — setting the letter property to one of: F, I, L, N, P, T, U, V, W, X, Y and Z.

Pentomino: Arrangement

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One of the ways that Pentominoes can be used is to construct a single large rectangle.

Such a rectange can be 6 by 10 squares in size, as shown below, or 5 x 12 or 4 x 15 or 3 x 20.

See the pentominoes.py script for how this is done.