You may prefer enneagon, but the term nonagon goes back centuries (OED says 1688), and I bet you will find the Latin hybrid version (nonagon) in more US geometry books than enneagon.
I think it's fine to say you prefer enneagon, but to say it is wrong because it is inconsistent means that we should also look at banishing triangle and quadrilateral. I respect John Conway and his research, but in English we have no Academie with 40 immortels who have the right to banish a word.
Rich Kleinschmidt
No, I prefer 9-gon. This question about fancy names for polygons recurs from time to time in various news groups, and John Conway has tried to lay it to rest with his clever list. However it has hardly any relevance to what mathematicians actually use. I regard the term "enneagon" as rather perverse, and "nonagon" as even more perverse.
Ken Pledger.