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I've made a tile grid where every face is disconnected from other faces ( no common vertices ). I would like to get a following effect:

enter image description here

But instead I get following:

enter image description here

How can use proportional editing for faces only, not vertices ?

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First you need to extrude all the faces individually.

enter image description here

Then select all the bottom vertices and hide them using H button to leave visible only the top faces and use proportional editing to move the faces up.

enter image description here

Then select all the faces, change Pivot Point to Individual Origins and scale on Z axis to zero using SZ0 buttons.

enter image description here

Then unhide hidden geometry with Alt+H shortcut.

enter image description here

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