In this paper we explore a contemporary conceptualization and creation of four, historical 14-pointed star polygon designs illustrated and analyzed in Plates 164 – 167 of Bourgoin's Arabic Geometrical Pattern and Design. We seek to determine how the original designer of these patterns may have determined, without mensuration, the proportion and placement of the star polygons comprising each pattern. We will do this by proposing a plausible Euclidean “point-joining” compass-and-straightedge reconstruction for each.