A Study on the Uniqueness of Self‑Fitting and Mutual Interfitting Properties in the Construction of Equilateral Rhombic Polyhedra

rhombus and mutual interfitting of two rhombi. Starting from the generating‑vector theory of zonohedra and combining the maximal size theorem of equiangular lines (Rankin’s theorem) with the inner‑product spectra of the symmetry groups of regular polyhedra, this paper carries out a rigorous mathematical derivation and determination of the uniqueness of the self‑fitting property of the golden rhombus and the mutual interfitting property of the honeycomb rhombus and the double‑Fibonacci rhombus. We establish a lemma that establishes a one‑to‑one correspondence between rhombus faces and generating vectors, thereby converting the geometric fitting problem into an algebraic classification problem of equiangular‑line inner‑product sets. Consequently, we prove that only the golden rhombus (acute angle ≈63.43°cosα=1/√5,) possesses the self‑fitting property, and that only the honeycomb rhombus (acute angle ≈70.53°, cosα=1/3) together with the double‑Fibonacci rhombus (acute angle ≈41.81°,cosα=√5/3) possess the mutual interfitting property. Systematic counter‑example analysis excludes all other candidate rhombi and rhombus pairs, and a set of operational criteria is established. This study provides a theoretical boundary for the classification of equilateral rhombic polyhedra.