# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 17th 2009

Jim Stasheff pointed out a reference that discusses categorifications of associahedra. I added the ref to associahedron

• CommentRowNumber2.
• CommentAuthorColin Tan
• CommentTimeMay 9th 2014

Urs, this link at associahedron to the reference by Forcey you mentioned is currently broken.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 9th 2014

• Stefan Forcey, Quotients of the multiplihedron as categorified associahedra, Homology Homotopy Appl. Volume 10, Number 2 (2008), 227-256. (Euclid)
• CommentRowNumber4.
• CommentAuthorTodd_Trimble
• CommentTimeMar 17th 2015

I have added an abstract description of (barycentrically subdivided) associahedra, in terms of a bar construction, to the definition section of associahedron. This is actually a definition, which wasn’t really there before.

• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeMar 17th 2015

Nice!

1. I added a pointer/short description of Loday’s concrete realization of the associahedron as a convex hull of integer coordinates. I wonder how it relates to the construction Todd gave above?

• CommentRowNumber7.
• CommentAuthorTodd_Trimble
• CommentTimeNov 25th 2015

Good question. I believe Stefan Forcey has worked on bridging these sorts of abstract and concrete descriptions of polyhedra that arise in operadic combinatorics. You’re right that some effort to go into this should be entered at the nLab.

2. The links under “Rotatable illustrations of some Stasheff polyhedra…” seem to be dead. I could be wrong, so I won’t remove them, although I did explore them and could not find rotatable polyhedra. For separate reasons I recently made a 3D rotatable associahedra app for the first 10 associahedra, and given that these links seem to be dead, I thought I would share.

Anonymous

3. That app is very cool! Thanks for adding! It brings home the impossibility of dealing with higher categories purely combinatorically! I agree that we can tweak the old links, I will do that now.

• CommentRowNumber10.
• CommentAuthorRichard Williamson
• CommentTimeOct 17th 2020
• (edited Oct 17th 2020)

Updating and otherwise tweaking links to visualisations of Stasheff polyhedra, giving preference to the fantastic app linked to in the previous edit!

4. The picture of $K_4$ doesn’t display too well on a mobile. We should replace it by a Tikz figure; I think I have already created such a figure somewhere else on the nLab, I’ll see if I can find it later (or someone else is welcome to do so if they have time!).