In today’s How to Tile blog, we tell you everything you need to know about aperiodic tiling and how best to lay it to achieve a great finish! 

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Aperiodic tiling is a branch of mathematics concerned with tiles as units composed of shapes, forming an irregular pattern.

Aperiodic tiling cannot repeat themselves to form a pattern, they simply continue infinitely creating an ever-changing pattern.


Aperiodic tiling is sometimes called forbidden symmetry as it challenges the human association between repetition and symmetry.

The defining trait of an aperiodic tiling is that whilst they have symmetrical qualities, they are not entirely symmetrical. The most famous example of an aperiodic tiling is Penrose Tiling.

Penrose Tiles are popular in bathrooms and have even been used for tiling large floor spaces such as universities.

Due to the irregular pattern of aperiodic tiling, laying tiles in such a manner will be much more complicated than your standard symmetrical tiling. However, it can be done and the principles of tiling remain the same.

You will need to prepare your underlayment, substrate, mix your adhesive to lay your tile and grout to hand ready to apply, as well as your tools of course.


In this blog on how to lay aperiodic tiling, we will be referring to the Penrose Tiling. They are the most straightforward, containing only two prototiles- the dart and kite, the most common Penrose Tiling.

These are formed of two triangles each, called Robinson’s triangles. They are both quadrilaterals which when combined form a rhombus. A shape where all four sides have the same length and opposite sides are parallel.

aperiodic tiling

Laying Penrose Tiling requires a lot of planning and hard work, more so than periodic tiling. This is due to the complex nature of the pattern which does not adhere to the rules of translational symmetry.

There are three ways to begin a Penrose Tiling. Using the dart, kite or dart and kite together you can start the pattern with the following shapes: star, sun, ace, deuce, jack, king and queen.

It should be noted that there are an infinite number of Penrose Tiling combinations for you to choose from. You can find some generators online.

aperiodic tiling

The sun and the star possess global pentagonal symmetry and higher order versions of these shapes can be obtained via deflation, adding greater detail to the tiling.


When it comes to cutting your tiles to shape, fortunately there are no curves in the dart and kite Penrose Tile design. So the process itself is relatively straightforward.

To achieve a nice clean edge, use a wet saw or an angle grinder to cut the tiles. Some improvisation will be involved towards the end of your installation. So, you will need to cut the outer tiles to fit the perimeter of the tiling area.

This is not unusual in tiling, however due to the infinite nature of aperiodic tiles, the entirety of the outer area of the tiles will not align naturally with the perimeter of the tiling area. Therefore, will need to be cut to fit inside the surface area.

To make these cuts we recommend using either a RUBI cutter or angle grinder and RUBI diamond blade:

ND-200 wet cutter

ND-200 Wet CutterThe ND-200 is a portable, lightweight, and compact cutter ideal for working in small spaces and on smaller sized tiles. The ND-200 will allow you to easily make precise and intricate cuts if needed to easily fit your tiles, with a water-cooling system to keep the blade cool while cutting.

Angle grinder and RUBI diamond blade

An angle grinder is also a great alternative when cutting these aperiodic shapes, due to its lightweight and portable size. The blade needed for your grinder will depend on the type of material you are cutting.

aperiodic tiling

For ceramic tile, we recommend using the CSV Pro blade.

This blade is the best choice for dry cutting with a grinder for all types of ceramic tiles.


aperiodic tilingFor harder materials such as porcelain, we recommend using the TVA diamond blade. It is specifically designed for cutting hard materials such as porcelain tile.

The specific design of this blade offers greater speed for cutting harder materials without sacrificing the quality of your finish.


The simplest manner of laying the tiles would be to first print the pattern on a page of grid paper, with each grid representing a tile, then cut the tiles accordingly.

You’ll want to design a pattern using computer software as it will be much more effective than something hand drawn. You could make use of formulae to come up with designs quickly and efficiently.

You can mark the tiles with arcs of different colours. Then when matching the arcs together in a Penrose Tile pattern, you should begin to see a pattern form. Once you have confirmed the pattern for your project, you can begin to lay the tiles.

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When it comes to laying aperiodic tiling, we recommend starting your pattern in the centre of the tiled area and working your way outwards. This is because the pattern will develop outwardly from a single shape. From there, follow the blueprint and lay the tiles as you would normally.

Make sure when laying your tile onto the adhesive, to apply firm, even pressure to the tile, inserting spacers between each tile for the grout. Once grouted, you may also want to apply sealing as this will protect the grout and give your tiles a nice, polished look. 

Always remember to clean as you go, making sure to wipe away any excess grout from the tile.


Stronger materials are easier to work with in this case as cutting the dart made of weaker materials may lead to manufacturing difficulties.

Penrose Tilings are also three-colourable, meaning each of its three ‘faces’ can be coloured differently and retain their pattern, emphasising the 3D nature of the rhombus.

This works in your favour if you are open to more colour combinations for your floor or surface area. It should be noted that Penrose Tile patterns can have two colours if desired.

Penrose Tiles are a mathematical wonder, allowing for an infinite number of combinations tiling designs to choose from based on only two tiles. They make for an excellent surface area and are not mass produced due to each pattern’s unique structure. It allows you to completely personalise your tiled surface and make a statement.

Whilst this is more complicated than your average symmetrical tiling pattern, there are plenty of Penrose Tiling generators on the internet to save you time planning your aperiodic tiled surface, so why not give it a try!

We hope you’ve found our blog on How to Lay Aperiodic tiling useful!

For more tiling tips and tricks on how to tile, please check out more of our blog articles here.

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