Starburst - a 3.8.24 tiling

The Starburst tiling is constructed from a "jewel" that is a 24-gon with four bites taken out of it. Using the 12-rhomb (red) and the 24-rhomb (brown gold), I have added back the bites to create a very interesting (and beautiful) decomposition of the 24-gon.

This tiling, sent to me by Robert Fathauer, has a central star constructed from eight 8-rhombs. As is often the case, the tiling is constructed mainly from a convex polygon with some "bites" taken out of it. When the bites are restored, the convex polygon turns out to be the 24-gon itself!

Like many of the Fathauer tilings, the Starburst tiling is constructed from a nutshell. In this case, the nutshell contains four 24-gons alternating with four octagons:

If we replace the 24-gons in the Starburst tiling with the 24-gon decomposition and the octagon is also decomposed into rhombs, we can derive a beautiful plane tiling that consists entirely of rhombs and triangles. I've included an image of this tiling as well below.


Translational Unit


Skeleton tiling

Tiling (Black and white)

Translational Unit (Black and white)

Derived rhomb and triangle tiling

In order to construct this tiling we also need the 24-rhomb (coloured brown gold).