This work presents an investigation into the geometric structure of star polygons inscribed in a circle. The study is motivated by a practical objective: to develop intuitive and systematic methods for constructing these figures manually. Starting from Schläfli notation, we introduce a set of mathematical variables that describe key structural properties of star polygons and allow us to identify recurring geometric patterns. We define and analyze several classes of patterns, proposing a general categorization based on relationships between these variables. Through explicit constructions and mathematical derivations, we show how different patterns emerge and how they can be systematically described. Special attention is given to limit cases, whose behavior is analyzed to clarify apparent ambiguities and confirm their geometric consistency. This work has a dual nature: on one hand, it provides practical tools for constructing star polygons; on the other, it contributes to a deeper theoretical understanding of their geometric properties and pattern structures.