A unified vision of the symmetric coupling of angular momenta and of the
quantum mechanical volume operator is illustrated. The focus is on the quantum
mechanical angular momentum theory of Wigner's 6j symbols and on the volume
operator of the symmetric coupling in spin network approaches: here, crucial to
our presentation are an appreciation of the role of the Racah sum rule and the
simplification arising from the use of Regge symmetry. The projective geometry
approach permits the introduction of a symmetric representation of a network of
seven spins or angular momenta. Results of extensive computational
investigations are summarized, presented and briefly discussed.Comment: 15 pages, 10 figures, presented at ICCSA 2014, 14th International
Conference on Computational Science and Application
