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# 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.

### Derived rhomb and triangle tiling

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