In this talk, I will discuss how the two geometric notions "fan" and "monoid" can be very fruitful for the understanding of the monopole formula for 3d N=4 gauge theories. After a brief reminder of the monopole formula, I will introduce the matter fan and reorganise the monopole formula accordingly. I then discuss the resulting benefits such as: (1) Explicit expressions for the Hilbert series built from well-studied constituents. (2) Proof that the order of the pole at t=1 and t → ∞ equals the complex or quaternionic dimension of the Coulomb branch. (3) Identification of a sufficient set of chiral ring generators.