  The Helon model identifies Standard Model quarks and leptons with certain
framed braids joined together at both ends by a connecting node (disk). These
surfaces with boundary are called braided 3-belts (or simply belts). Twisting
and braiding of ribbons composing braided 3-belts are interchangeable, and it
was shown in the literature that any braided 3-belt can be written in a pure
twist form, 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. For these braids an
algorithm to calculate the braid word is determined which allows the braid only
word of every braided 3-belt to be written in a canonical form. It is
furthermore demonstrated that the set of braided 3-belts do not form a group,
due to a lack of isogeny.
  The conditions under which the boundary of a braided 3-belt is a knot are
determined, and a formula for the Jones polynomial for knotted boundaries is
derived. Considering knotted boundaries makes it possible to relate the Helon
model to a model of quarks and leptons in terms of quantum trefoil knots,
understood as representation of the quantum group SUq(2). Associating
representations of a quantum group to the boundary of braided belts provides a
possible means of developing the gauge symmetries of interacting braided belts
in future work.

Geometric Topology;Algebraic Topology