Abstract Algebra Adventures Part 6: The n-cubic groups

When it comes to Group Theory, this series has so far focused on cyclic groups. We've talked much about the orthoplexic groups and the simplexic groups, both of which are cyclic.

But we cannot talk of two infinite polytope families (the orthoplexes and the simplexes) without talking about the third infinite polytope family: the n-cubes. It's just that, well, in the context of polytopic algebras, n-cubes are a bit more special, and it's taken me much longer to figure out how they fit in our puzzle.

So, how do we go about constructing groups whose convex hulls are n-cubes? Do such groups even exist in \(\mathbb{X}_n\)?

The Polytopic Algebra Wiki

Just wanted to announce that I created a wiki for the stuff I talked about in my Abstract Algebra Adventures series. The new under-construction "Polytopic Algebra Wiki" can be seen at https://polytopic.miraheze.org.

I'll be taking it slow translating my rough ideas into a wiki format. Right now the basic gist is mostly there. I've learned a lot since writing Part 5 of the series, and not only have I gained more interesting ways of describing polytopic algebras (which I'll incorporate in the blog soon), but I also have enough material to write Part 6 of the blog series! The wiki should help me record as much of this knowledge as possible until I hit another wall, then I'll write the blog post to describe what I learned in a more bloggy kind of way. 😋