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I am totally new to blender, so please forgive me if it is a dumb question.

When I add a face by pressing 'F', I found out it adds an vertices to where it seems to be middle position of selected points.

It doesn't show up in vertex select mode, but I can see it on Face select mode. Because it doesn't show up in vertex select mode, I tried to delete it but I can't.

and it mess up subdivision surface.

I am so confused why it is happening, please help. Thank you!

enter image description here I select vertices to add face.

enter image description here Pressed F and looks perfect.

enter image description here But when I change to face select mode, yellow dot appears inside a circle with green and red arrows on it.

enter image description here

end up with weird shape because of that dot. :(

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That orange square you see is not a vertex, but a "control point" that represents your face in Face selection mode (it's placed outside the actual face because the face is concave!). Also, it is not the reason your Subsurf looks odd.

Subdivision surface looks bad in general with faces with high number of edges, especially if they are concave.

The particular case of the base of an anvil has been asked dozen of times. Not all of them have the exact same issue (though they are similar), but the first one definitely is like your case:

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Unfortunately, using subdivision on a mesh like that one, wont usually work if you work off edges and vertices, blender doesn't like that.

start from the top and work to the base, that's the way I like to work, and it allows me to scale things better. work off what you have though, perhaps don't subdivide, but use the cut tool in editor mode and smooth it yourself, to make it look more human.

also the dot is the center of the entire thing? if it's yellow and you've selected the mesh.

using F to make faces and subdivision aren't good friends!

( i'm not a pro, take what I say with a grain of salt, it might not work! )

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