Definition. (Wikipedia) A crystal is a solid material whose constituents are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.

We will discuss the above definition in the context where the the solid material is a basis of a vector space and the highly ordered microscopic structure is a colored directed graph. Then we will explore how crystals extend to all directions, in particular, how they connect something that is supposed to be easy (linear algebra) to something that is supposed to be even easier (combinatorics) through something that may not sound so easy (quantum groups at absolute zero temperature).