User:OfficialURL/To-do list

A personal to-do list of articles I want to write, expand, or rewrite.

Need writing

 * Realization: add info on vertex-embeddings and maps.
 * Dimension: currently empty, find a basic definition and some citations.
 * Hypertope: Pretty much empty, add the info from that one slideshow.
 * Flag graph: Should be simple enough. Maybe an article on colored graphs might be needed too.
 * Complex, Maniplex: Pretty much empty, add info from the complicated paper and the introductory one.
 * Field: Useful for the article on conjugates.
 * Vector space: Highly relevant for polytopes.
 * Coxeter group, C-group: Highly important articles for a thing full of misconceptions.
 * Group presentation: Needed for the previous articles.
 * Wythoffians: Might be hard to write this one since I'm currently researching these, but I'd still like to give it a shot.
 * 2ᴷ polytope: Would be cool.
 * Comb product: Almost empty, we could copy large parts of it from the articles for the other products.
 * Polytope product: We could summarize the main results from this cool paper.
 * Compound, connectivity: Very important articles that don't exist for some reason.
 * Lattice polytope: Short (and separate) articles on both meanings of the word would be nice.
 * Volume: This one would largely be original research, but whatever.
 * Density: Related to the previous one.
 * Interior: Related to both of the previous ones.
 * Automorphism group: A short and sweet article.
 * Group action: Another short and sweet article.
 * Quaternion: A highly relevant article to swirlchora.
 * Complex numbers, Octonions: We might as well.
 * Congruence, similarity: An excuse to throw the words isomorphism and isometry at the very end of the article!

Need expansion

 * Conjugate: Since Klitzing and Bowers had a different notion of conjugation, it might be worth adding it and examining what they have in common.
 * Flag: It's already pretty good, but maybe we should add the related meaning on hypertopes?
 * Symmetry: Go over the different kinds of symmetries (reflections, rotations, etc.), separate the part on symmetry groups.
 * Symmetry group: A short and sweet article, if we can get ourselves to agree what counts as a symmetry group. There's messy cases, like points and certain cursed Grünbaumians.
 * Hopf fibration: We should talk about the other Hopf fibrations and their symmetry groups. This paper will be immensely useful.
 * Self-dual: We should talk about polarities.

Need rewriting

 * Coxeter diagram: Just no. This article was made at a time where we barely understood the mathematical theory behind these. This needs to be divided into many other articles.
 * Polytope: We shouldn't assume that the word "polytope" is meaningless. It has a lot of meanings, sure, but all of these are established and pretty much unambiguous in context. We should go over commonalities, then link to articles on the different precise notions of the word.
 * Regular polytope: This is just a huge listacle. There's so many nice results on regular polytopes we should talk about instead (i.e. the entire first chapter of ARP).
 * Convex polytopes: Convex polytopes are a very specific and interesting object and we should talk about that. Maybe separate the property of embeddings into another article titled convexity?
 * Step prism: We discovered a much wider class of these a while back. This article needs a total rewrite in my opinion.
 * Swirlchoron: The intro is alright but the rest of the article is just a huge listacle. Not cool. We should also go into their relations with quaternions.
 * Schläfli symbol: Written in a weird tone, and also we should probably explain what Schläfli type is within that article.
 * Quasiregular polytope: Also a mess. I need to do some research on this.