Geometric Classification of Spin Derived from the Orientation Structure of the 5-Dimensional Orthoplex

Puntos clave

• The aim is to classify different spin quantum numbers using the geometric properties of a 5-dimensional orthoplex.
• Derivation of spin quantum numbers from the orientation structure of a 5-dimensional orthoplex.
• Use of integer geometry to establish the connection between spin and geometric properties.
• Application of S3 symmetry for particle generations decomposition.
• Complete set of representable spin quantum numbers derived: s = 0, 1/2, 1, 3/2, 2, 5/2.
• Geometric distinction between fermions and bosons identified.
• Establishment of force directionality stems from sign-reversal parity.