In a pair of papers, Robert Ghrist constructed two families of branched two-manifolds, or knot templates, that are universal. That is, each template contains an isotopic copy of every knot (and link) type as a periodic orbit of the corresponding semiflow. A common feature of these families is an even number of half-twists in one of the strips. We eliminate the requirement that the number of half-twists be even and call the enlarged family of templates Ghrist templates. We demonstrate that all Ghrist templates are universal, specifically those containing an odd number of half-twists. We then use this result to briefly examine the knot structure of a geometric model of a system of differential equations on [Formula: see text] known as the Newton–Leipnik equations.