Zero Point Spiral v5: Projection, Layering, and Observed Difference in the 600-cell
Year: 2026
Type: preprint
Abstract: This paper is a constructive, computational case study showing how the observation-operator model of ZPS (Zero Point Spiral, v4 §§5–6) concretely manifests in the three-dimensional projection of the four-dimensional regular polytope, the 600-cell. Decomposing the 600-cell into layers by latitude from a polar axis yields the concentric structure 1+12+20+12+30+12+20+12+1 = 120 , and the latitude-0.5 layer forms a regular dodecahedron. The edges of this dodecahedron are not newly created by projection; they coincide with the native edges of the 600-cell restricted to the layer (confirmed). The five-tetrahedra compounds within the layer split into two chiral systems, and their visible left/right assignment is relative to the choice of polar axis as an observation window: proper rotations fixing the window cannot exchange them (because the stabilizer is the icosahedral rotation group I ), whereas a four-dimensional rotation moving the window carries one to the mirror compound of another layer. This paper does not prove ZPS; rather, it exemplifies on the 600-cell that while the symmetry of a higher-dimensional structure is intrinsic, the visibility, sign, and handedness of its differences appear relative to the observation window.
Author: Kamiki, Sana
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171297515