We propose a comprehensive geometric and algebraic framework that unifies the empirical Koide mass formula with a recursive pentagram structure governed by the golden ratio φ. Within this framework, five Koide triplets—corresponding to charged leptons, neutrinos, up-type quarks, down-type quarks, and a conjectured composite sector—are embedded into the self-similar isosceles triangles of a fractal pentagram. This construction reveals a hierarchical φ-scaling symmetry that systematically organizes particle masses across the Standard Model spectrum. The embedding is formalized through the dimensionless Pellis Function, which generates recursive φ-based relations linking mass ratios, fractal structures, and fine-structure patterns. These results indicate that the Koide relation is not an isolated numerical coincidence, but rather a manifestation of a deeper φ-governed fractal symmetry, offering new insights into mass generation, potential unification beyond the Standard Model, and the underlying mathematical structure of nature. We further introduce the Golden Pentagon of Masses, a novel framework that formalizes the embedding of Koide triplets into the fractal pentagram. Each triplet is assigned to a hierarchical recursion level, revealing systematic φ-scaling across fermion sectors. This construction provides a geometric and algebraic unification of mass hierarchies, where the Pellis Function generates recursive relations connecting mass ratios, fractal geometry, and fundamental constants. In addition, we present the Higgs—Pellis Coupling Fractal Matrix (HPFM), a universal framework for the Yukawa sector of the Standard Model. In this approach, fermion masses emerge from a self-similar, fractal matrix governed by powers of φ. This structure naturally reproduces hierarchical mass patterns, Koide-like relations, and fractal textures within the Higgs sector. The HPFM framework is universally applicable to quarks, leptons, and neutrinos and can be extended to seesaw mechanisms and beyond-Standard-Model scenarios. Finally, we demonstrate that the inverse fine-structure constant arises from the evaluation of the Pellis Function at the golden ratio φ, suggesting a unified fractal origin for fundamental physical constants. Together, these results provide a cohesive visual and algebraic unification of mass structures in the Standard Model and beyond, highlighting the interplay between geometry, number theory, and fundamental physics.