Some years ago, the author constructed a family of hyperbolic knots \(K(\ell ,m,n,p)\) , with the property of having a half-integral toroidal surgery, that is a r/2-Dehn surgery which produces a manifold containing an incompressible torus. This was done by means of sums of tangles and double branched covers. In this paper, we give an explicit construction of a subfamily of these knots, that is, a construction where we can see how the knots look in the 3-sphere.
