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I've taken a Torus and cut it in half, it works perfectly fine as you can see.

But if you go into Edit Mode, the bottom of the bagel half is made up of two faces, I want to get rid of the edges separating the faces and merge them into one whole face, how could I do this?

Thanks for your time and effort!

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    $\begingroup$ Neither it can be dissolved nor you should do that; ngons with empty areas without any supporting geometry likely aren't supported in Blender. But even if they were this is very bad idea of modeling as you can have a lot of unexpected problems just because of that simple geometry. Convert that ngon to quads/tris and it will work fine. What I will suggest to dissolve is that bunch of edge loops on the sides of the cylinder; they are mostly useless, keep only those which help preserve forms. $\endgroup$ – Mr Zak May 27 '17 at 9:37
  • $\begingroup$ ...but why you want to get rid of those edges? $\endgroup$ – m.ardito May 27 '17 at 11:18
  • $\begingroup$ @Mr Zak, but why is it a bad idea, what problems would actually occur if I didn't convert to tris/quads? I thought n-gons were better because they reduced the amount of needed edges in a mesh. $\endgroup$ – Flostin May 27 '17 at 17:27
  • $\begingroup$ First. Unwrapping will behave strange. Second, ngons are converted to tris automatically so you might find surface which behave strange. Furthermore, they aren't supported by some programs like game engines (not only), there will be just a hole. Also - blender.stackexchange.com/a/20816/1245, blender.stackexchange.com/q/89/1245. Ngons are not better. They are easier to keep track of while e.g. draft modeling. That depends on the mesh purpose, but once done, better convert them. $\endgroup$ – Mr Zak May 27 '17 at 18:22
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You should try to avoid ngons (an ngon is a face with more than 4 vertices), and keep your topology as quads.

Delete the two large faces in question.

enter image description here

Select the outer and inner edge loops:

enter image description here

Press the space bar and type bridge edge loops.

enter image description here

New faces will be created using quads:

enter image description here

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