A Kepler star: an octahedral cavity at the centre, eight tetrahedral rays on its faces. A tetrahedron is trapped inside. A ray flashes when the trapped tetrahedron touches its face. With no external influence all eight glow equally — a superposition; an influence dims them.
What the model shows. A tetrahedron of the same edge fits an octahedral cavity of the lattice exactly: its base lies on a face, its apex at the centre of the opposite face. There are eight positions, all equivalent. By the supergeometry principle a system with no reason to pick one occupies all of them at once: the probability of each, 1/8, is set by symmetry alone. The state spectrum is 1 : 3 : 3 : 1 (group O_h).
Graded quantumness. A uniform influence dims the rays 8 → 4 → 3 → 2 → 1. An influence that is itself symmetric among several positions cannot choose between them: a field along a cube axis stops at 4, an axial stretch at 2 (peanut), a squeeze at 6 (torus).
Status. Hypothesis. The model illustrates the supergeometry principle; it is not established physics. A preprint with a testable prediction (C₆₀ vs C₇₀) is in preparation.
Code. Every number on this page can be reproduced: supergeometry_table.py (the table of graded quantumness), cavity_geometry.py (the tetrahedron-in-cavity geometry), oh_states_8x7.py (symmetry decomposition of the states). Python with numpy (and scipy for the geometry script).