Try bisecting the polygon by connecting those two bottom points with the knife tool from that view, then look at it again or remap it. You've got a malformed polygon there (yes, this is your fault
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Anim8or is trying to fill that polygon the best it can, but in this instance it isn't producing the results you want. This is because you don't have all the points nearly on the same plane for a face with 6 points. Anim8or has to triangulate all faces internally no matter what, even though you might work with faces with more than 3 sides. Those "edges without the black line" you see is where it's triangulating it in order to "fill in the blank" you made. Keep making sloppy "blanks" like those, and it's no surprise that Anim8or will drop a turd on it. Typically try to stick with quads or triangles where possible and use ngons (for our case 5 or more sides) only if they rest on the same plane or near enough. When I say "plane", I mean that generally the entire face is "flat" unlike yours.
By the way, a tip or trick: If you want to find out how Anim8or would triangulate the mesh when exporting to .3ds, use those "edges without the black line" on the more unusual polygons like that, and manually triangulate the polygon with the knife tool if you don't like how Anim8or will do it.
