Hi Rachel - the problem here is with the layout / formation of the curves - in order for Network to work right the curves must form a grid layout where they can be unwrapped to a 2D pattern. It's similar to how on a 3D globe curves of longitude and latitude unwrap to horizontal and vertical lines on a 2D map.
In your current layout here it's not possible to get a 2D representation because of your 2 long curves crossing each other and then connecting back to the same base ring.
You can solve this by splitting the long curves (use the Edit > Trim command to cut them) so that they will share endpoints where they come together making a kind of "pole" region similar to the north pole or south pole on a globe.
Check out here for some links to previous discussions about Network curve layout:
http://moi3d.com/forum/index.php?webtag=MOI&msg=4384.4
And one that applies to your particular case:
http://moi3d.com/forum/index.php?webtag=MOI&msg=1778.6
- Michael
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