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Given: a mesh which forms one-n'th of a torus. I Alt-D-duplicate it, rotate the copy by 360°/n, and get the ends to meet up. Repeat n-1 times.

I have now a nicely symmetric object which I can edit further. This is not the problem.

The problem is that when I move a vertex at the border between copies, that nice alignment is destroyed. Obviously I cannot join the corresponding vertices; it's the same underlying mesh, after all..

Thus, how can I keep them in sync while editing? Repeating the edit steps on the "other" side is tedious, and snap-to-vertex doesn't help much either.

To clarify: I want to create a closed object with n-fold symmetry which stays closed and symmetric, no matter which vertex/edge/face I move. A normal torus will not stay symmetric. A 1/nth-torus with n-1 360°/n-rotated copies will not stay closed when I move a vertex/edge/face at the border.

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One point to note is that the term for a point in Blender is called a "vertex", not "vortex". – Thom Blair III Mar 24 '14 at 11:09
I think you should be using the "screw" modifier for this. – Alvin Wong Mar 24 '14 at 14:53
Are you simply talking about removing overlapping vertices? if so, A to select all vertices, then W > Removing Doubles. – Leon Cheung Mar 24 '14 at 16:35

You could merge the vertices by invoking the Remove Doubles operator

enter image description here

In your case you could create the torus without duplicated vertices, starting with an e.g. an 1/8th

enter image description here

By rotating using the Spin Tool Alt-R in Edit Mode

enter image description here

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Alt-R does not seem to do anything in my version of Blender. In any case, did you actually try moving e.g. the top-most vertex after this? Did that action leave a hole in the torus? – Matthias Urlichs Mar 24 '14 at 17:08
@MatthiasUrlichs You need to be in Edit Mode, and yes you won't have duplicated vertices with the settings used in the image. – stacker Mar 24 '14 at 20:05

I don't completely understand the problem you are encountering, but here are a few things you might try:

  1. While in Edit mode, before you start modeling (such as duplicating your torus sections) turn on "Automatically merge vertices moved to the same location":

    enter image description here

    This makes sure you won't have double, non-merged vertices in the same spot, thus you won't have to use Remove Doubles later on.

  2. When you use ALTD to duplicate the torus section, you are creating what is called a Linked Duplicate. With Linked Duplicates, whenever you modify the section, ALL of the sections will be effected, as shown here:

    enter image description here

    However, if you don't want this to happen, use SHIFTD to create non-linked Duplicates. With these kinds of Duplicates, when you edit one, the others remain unedited, as shown here:

    enter image description here

If you want to learn more about the differences between Duplicates and Linked Duplicates, you can read more about them here:

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Thanks, but I do know the difference between a duplicate and a linked duplicate. The point is that auto-merging vertices does not work for linked duplicates. In your first linked-duplicate example, you moved a random vertex on the surface of the quarter-torus. That obviously works. However, moving a vertex on the very top (or left etc.), where the duplicates join will leave a hole. – Matthias Urlichs Mar 24 '14 at 16:54

Try using an Array modifier:

  1. Add a torus and delete three quarters of it:

    enter image description here

  2. Add an empty and rotate it 90° around the Z (or whatever axis to which the torus is aligned)

    enter image description here

  3. Add an array modifier to the torus, with Object offset enabled and the empty selected as the offset object:

    enter image description here

By using the 3D cursor as the pivot point and being suitably careful about how you move your vertices maintaining a manifold mesh shouldn't be too hard. Another advantage to the array modifier is that it updates in edit mode.

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