In 1890, Lothar Heffter described a complete map with nine regions on a surface of genus three. Heffter used a table of numbers to present his map, which makes it very hard to visualize. This paper shows how we used Heffter's numerical description to sew a physical model of Heffter's map that clearly shows it is indeed drawn on a surface of genus three. The sewn model also reveals other interesting features of this map. In addition, we discuss models we have sewn of two other distinct nine region complete maps on a genus three surface.