Laminations are a combinatorial and topological model for studying the Julia sets of complex polynomials. Every complex polynomial of degree d has d fixed points, counted with multiplicity. From the point of view of laminations, at most d-1, of these fixed points are peripheral (approachable from outside the Julia set of the polynomial). Hence, at least one of the d fixed points is “hidden” from the laminational point of view. The purpose of this study is to identify, classify and count the possible fixed point portraits for any lamination of degree d. We will identify the “simplest” lamination for a given fixed point portrait and will show that there are polynomials that have these simplest laminations. An application of fixed point portraits is to establish a correspondence between locally unicritical laminations and locally maximally critical laminations with rotational polygons. This application is a joint work with Brittany E. Burdette.