Vertex locations of Dessin w/h Circle packing in Discrete Dessin d'Enfant

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I'm reading the following paper. Bowers, Philip L., and Kenneth Stephenson. Uniformizing Dessins and BelyiMaps via Circle Packing. Vol. 170. No. 805. American Mathematical Soc., 2004.

In the paper, Fig.3 is supposed to represent the dessin in Fig.1 (Right hand-side) but I can't seem to figure out the vertix locations of $\infty$-vertex.

** In fig.3 below, following this paper I use a solid dot to mark 0-vertices, a small x to denote 1-vertices, and the empty circle to represent $\infty$-vertices.

my attempt of marking the vertex locations in Fig.3

Here, (hopefully) I could find the locations of 0 and 1 vertices. but i'm not sure which of the circles inside the area surrounded by the thick line includes $\infty$-vertex.

Can someone help? enter image description here