In this paper we will explore one of the Tashkent Scrolls' repeat units, that, when replicated using symmetry operations, creates an overall pattern consisting of ``nearly regular'' nine-pointed, regular twelve-pointed and irregularly-shaped pentagonal star polygons. We seek to determine how the original designer of this pattern may have determined, without mensuration, the proportion and placement of the star polygons comprising the design. We will do this by proposing a plausible Euclidean ``point-joining'' compass-and-straightedge reconstruction.