Linking the geometric mass hierarchy with threefold family replication

A link is established between the observed (approximate) geometric mass hie rarchy of quarks and leptons and the triangular structure of their tenable flavour representations. This singles out SU(3)(H) as the horizontal flavou r group, thereby linking the Fermi mass hierarchy with the threefold family replication. These linkages are exploited within a flavour-chiral SU(3)(H) model, with fermions and Higgs bosons in the (3) under bar + <(6*)under ba r> representation. The model is left-right symmetric and utilizes the unive rsal see-saw mechanism with a geometric mass suppression pattern. Given cer tain assumptions, the model produces the following mass-ratio (rather than square-mass-ratio) mixing angle relations V-cb = -V-ts = m(s)/m(b) + m(c)/m (t), V-ub = (2m(c)/m(t) - m(s)/m(b))theta(C), V-td = (2m(s)/m(b) - m(c)/m(t ))theta(C), and fixes the m(u)/m(d) ratio.