Polycairo tiling

I have lately been experimenting with shapes composed of Cairo pentagons, with the aid of the  Polyform Puzzle Solver by Jaap Scherphuis.  One of the most interesting of these, is the fish.  Alain Nicholas worked his magic on it, creating a piranha, soon to be shown on his amazing site… http://en.tessellations-nicolas.com/

Piranha

 

It can produce aperiodic tilings within a square border of various sizes.

1a-aperiodic with border

 

This example displays the frequency and placement of rotations and mirrors.

DS-Cairo10

 

Smaller motifs can be arranged in different ways.  The bottom example had me fooled at first – the two images are actually mirrors of each other.

Cairo motif examples small

 

Here’s another polycairo made up of 12 Cairo pentagons.  It is easier to tessellate than the fish, as you only have to deal with rotations, due to its mirror symmetry

Goat

 

… and here’s the artwork that Alain Nicholas created from it – thank you kind Sir!

Nicholas-billy goat

 

A chaotic arrangement of the tiles.

Goat1

 

I believe this last example can only tile periodically but in an interesting way.

Cairo-8 rots

 

The pattern uses all four rotations and their mirrors.

Cairo-8a rotations

 

Thank you to David Bailey for helping out.  His site on Escher-like tessellations and Cairo tiling is well worth a visit… http://www.tess-elation.co.uk/new-hom

 

 

 

 

 

 

 

 

 

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s