For a century, physicists have written the gravitational constant G as a number, fitted to experiment and otherwise unexplained. Pentagon Physics asked whether G could instead be derived from the algebraic structure of a single finite group.
Pentagon Physics Gravitational Potential as a Class Function on the 600-Cell. For a century, physicists have written the gravitational constant G as a number, fitted to experiment and otherwise unexplained. Pentagon Physics asked whether G could instead be derived from the algebraic structure of a single finite group. A closed-form formula for the gravitational potential of the 600-cell architecture is presented, where every coefficient is determined by the algebra of the binary icosahedral group. The discrete Green's function decomposes exactly as a sum over eight non-trivial irreducible representations. The four integers appearing in the gravitational coupling formula are singled out by the architecture itself through representation theory. Gravity, gauge structure, and the framework's constants are written in the same alphabet because they share the same finite group. The result is exact, falsifiable, and reproducible in approximately 0.1 seconds on a standard laptop using the supplementary script.