Nested Bipyramid Solar System: Planetary Distances from Standing Wave Harmonics in a Hexagonal Cavity

We show that planetary orbital distances emerge as convergence points of standing wave harmonics inside a hexagonal bipyramid cavity centered on the Sun. The cavity radius R is derived from two inputs: the Sun's measured oscillation period (329 seconds) and the speed of light, yielding R = 1.000 AU with zero free parameters. Trapped harmonics predict inner planet positions (Mars at 0.0% error), while the pass-through fundamental wavelength predicts all four outer planets from a single number (Jupiter 2.5%, Saturn 3.1%, Uranus 0.2%, Neptune 1.2%). The cavity acts as a frequency filter: short wavelengths build rocky planets, long wavelengths build gas giants. Successive cavities nest with scale factor 16/3, predicting the asteroid belt, Kuiper cliff (3.1%), and heliopause as boundary zones. Each planet defines its own nested bipyramid, capturing exactly one new frequency band — paralleling electron shell filling in atomic physics. Companion paper to the Hexagonal Bipyramid Wave Geometry framework. Part of the Dimensional Oscillation Theory (DOT) research program.