How many initial monomial ideals does a homogeneous ideal have? We are to expect finitely many if our ideal is finitely generated, but what $\textit{are}$ they? The question turns out to have a sleek answer with the help of some fundamentals of polytopes! In this fan convention, I will introduce the basics of initial ideals, then polyhedra and fans. I will finish by guiding us to perhaps one of the spiciest ships in the algebraic combinatorics headcanon: the Gröbner fan. Join me in celebrating this power couple of my fandom, and perhaps you fellow Whovians, Sherlockians, and Potterheads will too become Gröbner fans.