Geometric-packability conjecture for the plane graphs \Theta_2, \Theta_3, and \Theta_4

Let $\mathcal{P}(G)$ denote the set of plane drawings of a graph $G$, and let $\Theta_2$, $\Theta_3$, and $\Theta_4$ be the three plane triangulated cycles shown in the source. A set of geometric graphs is geometric-packable if it can be asymptotically packed into every sequence of drawings of the complete graph. Geometric-packability conjecture. $\mathcal{P}(G)$ is geometric-packable when $G$ is any of $\Theta_2$, $\Theta_3$, and $\Theta_4$. The geometric-packing problem for these three graphs is described as open in the source, although the corresponding convex-packing statement is proved there.