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:

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!

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

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

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!