Where can I find a picture of the complete 9-map on a triple torus that corresponds to Heffter’s table? What I’m looking for is the analogue of
Figure 5 in the paper by Saul Stahl, The Othe Map Coloring Theorem, Mathematics Magazine 1985, which is a complete 8-map $M_8$ on the double torus $S_2$ that corresponds to Heffter’s table for n=8,
but for a complete 9-map $M_9$ on the triple torus $S_3$ that corresponds to the table for n=9 in Heffter’s paper, Uber das Problem der Nachbargebiete, Math. Ann. 1891.
 A: OK, having received no answer, I drew one such map myself. Took me a while. From Heffter’s table of the adjacency pattern to the corresponding picture involving 22 triangles and 1 hexagon, then to the complete 9-graph on a decent representation of the triple torus, and finally to the complete 9-map on the usual drawing of the triple torus, there are so many steps where you can get confused. In case anyone is interested, my map can be found here http://math.univ-lyon1.fr/~benzoni/complete-9-map-triple-torus.pdf. Do not hesitate to contact me if you have, or know of better drawings, or if you are interested in details of the construction.
A: I have a small group of friends who have been playing with maps on higher genus surfaces. We have made Heffter’s M_9 out of fabric and a different M_9 in origami. We have also made crochet models and some drawings. My M_8 and M_9 in origami will be in the JMM Mathematical Art Exhibition in Boston in January. We will also be displaying 3 different fabric M_9 (including Heffter’s) during the Fiber Arts Session Exhibit on Jan. 4. Any chance you are coming to the JMM? Here is a link to my origami models:
http://gallery.bridgesmathart.org/exhibitions/2023-joint-mathematics-meetings/etorrenc
