As a big fan of custom emoji, I'd be keen to see some more options on this instance, and have arranged with the admin to add a batch of new ones at some point soon: get your requests in and I'll try to include them!   
@stecks I guess you've seen the Petersen graph suggestions from @krystalguo , but here's the link so no one else has to look it up
https://mathstodon.xyz/@krystalguo/109337816332875145
Krystal Guo (@[email protected])

Attached: 3 images Can any of these be made into a #PetersenGraph emoji? @nilesjohnson @christianp @bmreiniger

Mathstodon

@stecks Sadly my server only seems to have this funky cat.

   

@stecks I'm a big fan of emojis too! I recommend this website: https://emojos.in/
You can type any instance domain there and find emoji codes.
I suggest to try mstdn.social and add some blobs and blobcats (๑>◡<๑)
Mastodon instance custom emoji list

@stecks for #Topology, or cool shapes in general, the #HopfFibration could be fun. For example, this picture is pretty recognizable. (Yes, I made it, but that's not the only reason to recommend it :)

https://commons.m.wikimedia.org/wiki/File:Hopf_Fibration.png

File:Hopf Fibration.png - Wikimedia Commons

@stecks Lastly, (apologies for the overload!) here are some ideas/requests for other people who might be interested:

- some classics: #PythagoreanTheorem , #MandelbrotSet , or #E8

- emoji for when you're thinking hard (maybe the orb from the orb-ponderer meme?)

- emoji for when something you thought was hard was actually easy!

- emoji for when something you thought was easy was actually hard!

@nilesjohnson Good suggestions! Any ideas for what these emoji might look like would be welcome 🙂
@stecks lol, yeah, I'd love to see them too :)
@nilesjohnson @stecks oooh, E8, I like it. Not sure how well the Petrie projection (https://en.wikipedia.org/wiki/E8_(mathematics)#/media/File:E8Petrie.svg) would work at emoji scale, but the Dynkin diagram could work...
E8 (mathematics) - Wikipedia

@stecks to my knowledge no site has a Rubik's cube emoji, if you add that you'll be my new favorite person ever. Assuming its in a legal state and has a logical color scheme
@SirWaffle @stecks I vote for this, and a varrubik emoji that has two stickers swapped
@christianp @stecks but the cube has even parity so that variant isn't possible unless you take it apart. Therefore it would be painful to look at
@SirWaffle @stecks it looks like emoji names can be more than 20 characters long. Are you thinking what I'm thinking?

@christianp

My immediate thought is probably complex and involves typing in an algorithm to achieve a specific cube state from a selection of emojis. Probably not what you're thinking though

@stecks

@christianp @SirWaffle @stecks one character per move and an emoji for every achievable cube state? Or you could represent only the visible faces, in at most \( 27 log_{256}(6) < 9 \) bytes.

@christianp

You know, solved rubik, scrambled rubik, and impossible rubik, fit three pretty frequent and distinct math moods: "it's worked out"; "it's not worked out but I know there's a way"; and "this is hopeless"

@SirWaffle @stecks

@stecks ooh, exciting! There must be loads of mathematical objects that would make good emojis. Polyhedra, tetrominos, dice – what else?
@robinhouston @stecks For dice there's already 🎲, and I see there are the die-face-n characters ⚀, ⚁, ⚂ etc but they're not technically emoji - no dice that aren't D6es, though, and no other polyhedra that I can see. Some of Anders Sandberg's "warning signs for tomorrow" might make good emoji? https://lifeboat.com/ex/warning.signs.for.tomorrow
Warning Signs for Tomorrow

The Book of Ratings rates danger symbols (via Ian Albert). Very enjoyable, and brings up the question of how to mark new threats. All the truly cool transhuman technologies are going to require warning signs.

@pozorvlak @stecks Surely we also need some of the better-known fractals? Sierpinski, Koch, Mandelbrot, etc
@robinhouston @stecks One for "space" in general, perhaps? The closest I can find in the official set is 🌌, "Milky Way".
@robinhouston @pozorvlak There's already  but it could definitely do with some friends!

@stecks if animated emoji are being considered, one of those looping Mandelbrot zooms would be rad! It could work for a mathy "mind blown" emote. (I mean, really any fractal zoom would be rad. Some will call Mandelbrot boring, but it's also classic and widely recognizable.)

@robinhouston @pozorvlak

@nilesjohnson @stecks @robinhouston I find animated emoji very distracting, so if they're being considered I'd love a way to disable the animations by default. I think 🤯 covers "mind blown" pretty well, but I agree that a more mathy alternative might also be nice.
@nilesjohnson @stecks @pozorvlak Other animated gifs on mastodon can be disabled with a setting: I assume that would apply to animated emoji too
@robinhouston @nilesjohnson @stecks aha, thanks! Sorry, I should have checked to see if that setting already existed before posting.
@pozorvlak @robinhouston @stecks I don't know that animated emoji can be disabled; I think they're treated differently than post attachments (e.g., there's no play/pause on emoji). Personally I have mixed feelings about them, so I can understand why some people wouldn't want them at all.
@pozorvlak @stecks @nilesjohnson Well, it should be easy to test this. We just need someone to add an animated emoji we can test it with.
@robinhouston @pozorvlak @nilesjohnson I got this reply earlier which contains some animated emoji, and for me these don't animate on the app but in-browser they animate when I hover over them? https://mastodon.world/@GavinSchofield/109353396204199913
Gavin (@[email protected])

@[email protected] Sadly my server only seems to have this funky cat. :ablobcatrainbow: :ablobcatrave: :apartyblobcat: :ablobcatbongo:

Mastodon

@stecks @robinhouston @pozorvlak hmmm, this seems to be another thing that depends on how the post is viewed. When I use the link you pasted (at mastodon.world), the animation goes when I hover anywhere over the post, but stops otherwise. When I use your OP link

https://mathstodon.xyz/@stecks/109353307781490216

and scroll through the replies, then the animation continues no matter where my cursor is.

Katie Steckles (@[email protected])

As a big fan of custom emoji, I'd be keen to see some more options on this instance, and have arranged with the admin to add a batch of new ones at some point soon: get your requests in and I'll try to include them! :aperiodical: :qed: :ramanujan:

Mathstodon
@nilesjohnson @stecks @robinhouston I get animation only when I hover over the toot in both places (on the web interface, haven't installed the app yet). Perfect!
@robinhouston @pozorvlak @stecks ha ha ha, that's one way :) Two seconds of internet searching seems to show that the official mastodon app has a setting for disabling animated emoji (separate from other animations), but the web client settings aren't the same. 🤷‍♂️

@nilesjohnson @stecks @robinhouston Reminds me of this highly random claim on Wikipedia:

(the paper cited is https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5886445/)

Did René Descartes Have Exploding Head Syndrome?

René Descartes (1596–1650), “the Father of Modern Philosophy” and advocate of mind-body dualism, had three successive dreams on November 10, 1619 that changed the trajectory of his life and the trajectory of human thought. ...

PubMed Central (PMC)
Discourse on the Matrix - pozorvlak - The Matrix (Movies) [Archive of Our Own]

An Archive of Our Own, a project of the Organization for Transformative Works

@robinhouston @stecks we used to have the "Nonstandard Spacetime" one up in the kitchen at a previous job. Good times. #startuplife
@stecks I kind of like 💯 except it's \(e^{2 i \pi}\cdot10^2\)
@stecks It needs work, but I am going to make this happen
@3j0hn incredible
@stecks I am sure this can be improved, but I should be doing work right now 😂 https://github.com/johnpmay/johnpmay/tree/main/100
johnpmay/100 at main · johnpmay/johnpmay

Config files for my GitHub profile. Contribute to johnpmay/johnpmay development by creating an account on GitHub.

GitHub
@stecks
A lot of overlap with other comments; I don't think I've seen these:
The basic glider from Conway's game of life.
More (combinatorial) graphs/hypergraphs/designs (Fano plane!).
Something statistical, but I don't know what.