Geometrical and topological considerations are increasingly important in fundamental physics. This book shows how a certain explicit realization of toroidal topology can expedite and simplify the modeling of the elementary particles of physics, in particular how the taxonomy, interactions and particle attributes of the Standard Model can be realized but without its quarks, gluons or “color”. The particles of the model featured herein exist as general-relativistically-compatible solitons, in and of an otherwise undistorted space-time continuum. The book emphasizes their geometry and topology and the symmetries of their taxonomical combination. What is achieved is, in effect, an amalgamation of two of the major responses to the particle explosion that bedeviled mid-century physicists, one the non-reductionist Sakata model and the other the Gell-Mann/Zwieg introduction of quarks. Readers with some familiarity with the Standard Model should find this book interesting and provocative.