Unlike the conventional treatment of the weak bosons in the Yang-Mills theory, which utilizes the Dirac equation for a point-like particle with no internal degrees of freedom, we propose an octonionic preon model to describe the internal dynamics of this vector0boson family with a photon as a isospin singlet, Z, W+, and W- bosons as a triplet. Instead of the Higgs mechanism, their masses are acquired from the internal dynamics of the chiral pair via strong spin-exchange couplings. Assuming couplings involving Gell-Mann’s lambda matrices, with no adjustable parameters, we predict mw/mz = sqrt(3)/2~ 0.87 vs. 0.88, a Weinberg angle of 300 vs. 29o, decay width mH/mW = sqrt (3)/2~ 0.87 vs. 0.84, and a Higgs boson, as a composite of W and Z bosons, with mw/mz = sqrt(7/3)~ 1.53 vs. 1.56 experimentally. These small discrepancies can be accounted for if weak interaction couplings are included. We use octonion operators to represent these particles and to elucidate their connections, and the topological structures' relations to fiber bare bundles and Hopf fibration. Moreover, we elucidate that our proposed preons are essentially the foundation for ding the hypercomplex algebra, and they are the building blocks for the composite particles that represent the topological structures in the higher-dimensional spacetime.