How to correct non-connected edges/faces? I've an object with edges that appear to be connected to a face, but when you move a faces touching the edge, it leaves a hole in the object:



I would expect the top and side faces to 'stretch' with the selected edge, when I move the selected edge (just like the bottom one).

This shape started out as a cube. I used only 'subdivide', moved edges to where I wanted them to be and tried the 'edge split' modifier. (what did I (likely) do wrong to create this mess?)

My question is: How do I repair the object?
This was caused by the Edge Split modifier, which, as its name infers, split your mesh at the edges. To fix it, select all the vertices and click the "Remove Doubles" button in the Tool Shelf.