Topological Crystals (Part 4)

Okay, let’s look at some examples of topological crystals. These are what got me excited in the first place. We’ll get some highly symmetrical crystals, often in higher-dimensional Euclidean spaces. The ‘triamond’, above, is a 3d example.

Review

First let me remind you how it works. We start with a connected graph This has a space $C_0(X,\mathbb{R})$ of 0-chains, which are formal linear combinations of vertices, and a space $C_1(X,\mathbb{R})$ of 1-chains, which are formal linear combinations of edges.