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
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
The symmetry and duality suddenly all become very apparent.
you've seen this thing as the 4-cocycle condition for tricategories
Power, Street] then you will know how geometrically unobvious it looks
drawn flattened out using 2-pasting diagrams. But build it in 3-D
it all becomes clear(er).
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
of a hand-drawn version all over the world!