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.
 * 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.
 * Automorphism group: A short and sweet 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.

Need rewriting

 * Coxeter diagram: Just no. This article was made at a time where I 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).