Hexagonal Bipyramid Wave Geometry: A Self-Selecting Container for Möbius Standing Waves

We demonstrate that a hexagonal bipyramid with a 30° face angle is the unique self-selecting geometry for a wave cavity that manufactures Möbius topology from simple anti-phase sources. The 30° angle simultaneously satisfies three independent constraints: the face inclination, the polar twist, and the resonant reflection angle. Simple opposite-phase waves emitted from the poles accumulate exactly π of twist over one complete circuit, becoming Möbius without any exotic source mechanism. The geometry produces constructive interference at the six hexagonal vertices with the fixed ratio h/R = 1/√3. Three force-like phase offsets (60°, 5.95°, 3.30°) are derived from the coupling between the Möbius twist and three…