This paper derives the complete classification of spin quantum numbers (s = 0, 1/2, 1, 3/2, 2, 5/2), the fermion-boson distinction, force directionality, and generation structure from the orientation structure of the 5-dimensional orthoplex. v2: Replaced prerequisite paper dependencies with a self-contained Assumption A (axis classification); removed Section 1.2 (metric integrality); generalized Proposition 4.1 to be scale-independent; updated references.
Noriaki Kihara (Sat,) studied this question.