It turns out that the ‘penguin’ nonagon can be constructed using any regular polygons, except pentagons and hexagons. I have ignored triangles and squares. You can view the original post here… https://hedraweb.wordpress.com/2021/04/02/penguin-nonagon/

So to recap, overlaps of polygons occur at midpoints between vertices. Only three polygons are needed but the visuals look quite attractive so I left them in. It is also worth noting that all other shapes produced within the regular polygon surrounds (except centres with odd numbers), can also tile but in less interesting ways.

The penguin will always be a nonagon but internal angles will change. The original penguin from overlapping decagons (below right) has identical internal angles for both feet (the only occurrence).

Because the pentadecagon is a factor of five, pentagon and decagon radials can still be achieved if you include central voids.

Here is one example with a pentagonal shaped void inner.

In the the examples below, I have used penguin from heptagons. I believe that concentric circles/loops, spirals and central voids will work in the same way with all regular polygons. However penguins from odd numbered polygons do not allow mirrored patterns.

Here I have produced two and three small spiral designs from the same penguin. Alas, a ‘galaxy’ spiral eluded me.