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Steps to reproduce the simpliest case:

  1. create a cube
  2. select one face and scale it to 0

enter image description here enter image description here enter image description here

The result looks like a pyramid, but obviously it's not, since we have 4 vertices (instead of 1) in the same place (if we, say, grab-X one, we get some mess, like in picture 4, not like in picture 5). How do I merge those into one? Or is there a better way to collapse a face into an edge with the same position?

enter image description here enter image description here

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    $\begingroup$ Your method is good, but it requires removing doubles (W) after scaling by 0 (select the whole mesh with A, then press W-->Remove Doubles). $\endgroup$ – Paul Gonet Oct 22 '16 at 15:23
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To illustrate what brasshat and Nils said, after you scale the top face to 0, switch to wireframe mode by pressing Z and then select the vertices using the box (press B) as shown below:

enter image description here

Then, press ALT+M to merge at center:

enter image description here

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  • $\begingroup$ The images you posted in your answer are unavailable. Please use StackExchange's image hosting next time. $\endgroup$ – Aaron Franke Sep 13 '19 at 21:31
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Select four top vertices, choose the edge select mode and press X-->Edge Collapse. enter image description here

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  • $\begingroup$ What if I'm starting from a situation where they are already inside of each other? There's no easy way to select all of them AFAIK. Also, I would like to do this for an entire mesh at once. $\endgroup$ – Aaron Franke Sep 13 '19 at 21:33
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After selecting all of the vertices you wish to merge, use the "merge" tool, called by use of the shortcut ALTM, and in this case, select the "at center" option. For more information, see the section on merging on the manual page https://www.blender.org/manual/modeling/meshes/editing/basics/deleting.html.

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  • $\begingroup$ Could you propose a convenient way to select all those? Somewhy box (B) doesn't work for me in the edit mode with mesh select mode = Vertex (when I surround the coinsiding vertices with box, only one remains selected). $\endgroup$ – YakovL Oct 22 '16 at 10:59
  • $\begingroup$ Most convenient way is tongo inti Face Select mode and select that face. Can then go back into vertex mode and vertices of that face will still be selected and you can use the Merge At Centre as described above. $\endgroup$ – Rich Sedman Oct 22 '16 at 19:20
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When you still have the cube select your top face and then press Alt M and select merge to middle. This should bring all of your top vertices together and merge them it one vertex.

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All of the other answers require you to manually select each of the vertices you want to merge, but are suboptimal if you already have them inside of each other. If you are starting from this state:

OP's image

Start by selecting all vertices using the A key, then use the By Distance option in the Alt+M or the Vertex -> Merge Vertices menu:

Merge By Distance

This will merge all vertices which are equal or nearly equal in position, such as you would get from creating a pyramid by scaling the top face by zero.

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Switch to wireframe mode and use box select or turn off "limit selection to visible" when in solid draw mode. That button is to the right of the face select mode button.

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