There are articles and other references to the straight strip 9 sided hexaflexagon called the nonahexaflexagon. There are straight strip flexagons for if the number of sides is divisible by 3. Dr. McIntosh describes these as flexagons with star maps. Be sure to read his papers on this topic as it is quite interesting. There is only one Map for this frieze pattern. All straight strip flexagons with more than 9 sides have multiple maps. See the Zodiac 12 sided flexagon for the 5 maps that will generate it. As with all my maps, the reverse face numbering is in the tables and can easily be marked on the back of the top triangles. Note that this flexagon has an odd number of sides and so the middle section has reverse numbering. Here it is:

More to come.........