A combing algorithm for orientable braided 3-belts

The Helon model identifies standard model quarks and leptons with framed braids composed of three ribbons joined together at both ends by a connecting node (disk). These surfaces with boundary are called braided 3-belts. The twisting and braiding of ribbons composing braided 3-belts are interchangeable, and any braided 3-belt can be written in a pure twist form with trivial braiding, specified by a vector of three multiples of half integers [a, b, c], a topological invariant. This paper identifies the set of braided 3-belts that can be written in a braid only form in which all twisting is eliminated instead. For these braids, an algorithm to calculate the braid word is determined which allows the braid word of every braided 3-belt to be written in a canonical form. It is furthermore demonstrated that the set of braided 3-belts does not form a group due to a lack of isogeny.