Build your own 5-associahedron!




Here is a serious piece of mathematics that also happens to be a nice object that you can cut out and make. All you need is a pair of scissors and some sellotape, and the handy pattern that you can download below:

associahedron.pdf


It's also on p.157 of Higher-Dimensional Categories: an illustrated guidebook, which I've just written with Aaron Lauda.


Tip: enlarge the template to A3 on a photocopier for a less fiddly model



Note for specialists:

Did it ever occur to you to build a 4-associahedron (also known as the 4-cocyle condition)?  If not, I urge you to try it as it's rather beautiful.  The symmetry and duality suddenly all become very apparent.  If you've seen this thing as the 4-cocycle condition for tricategories [Gordon, Power, Street] then you will know how geometrically unobvious it looks when drawn flattened out using 2-pasting diagrams.  But build it in 3-D and it all becomes clear(er).  

Eventually I will add some more detailed explanation about the thing here, but for the time being you can see an explanation in Higher-Dimensional Categories: an illustrated guidebook, Section 6.2.3, page 110.



Acknowledgement:

Thanks are due to Aaron Lauda
for making the associahedron template into a form that can be made widely available.  Until recently I been known to carry around a photocopy of a hand-drawn version all over the world!