I first came across this shape on a cover of a book, entitled ‘The Gentle Art of Filling Space (credited to Robert Reid, Michael Dowle and Anthony Steed).

I have since purchased the e-book of the same name (but different cover art) from Lulu Books, which was the less expensive option.

This intriguing shape is made up of six crowns (my drawings were based on observation only) and can be put together in many different ways.

The book only shows one radial tiling, so I spent some time exploring other possibilities. The examples below show a few ways the ‘birds’ can be tiled periodically (the last one is a hybrid).

A radial tiling can display two types of mirror symmetry (Robert Reid’s example is on the right) or can be mixed and matched to produce no symmetry (not shown).

By splitting the core of 10 ‘birds’, more chaotic patterns can evolve. Some show the same type of core displacement.

I believe all the patterns above, can expand forever. Part two will show examples of mirrored/non-mirrored core combinations.