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I'm trying to shrink the rim of this rock base so the top is slightly smaller than the bottom. But when I scale this selected rim, it pulls everything inward. it looks good from the exterior wall but the interior is slanted inwards.

Is there a way to shrink the top of the ring of cubes such that their vertical center remains in place, and the edges come inward?

The base of the structure: Base of a hawaiian style house

Exaggerated look at scaling the top: base of hawaiian structure scaled inwards

I'd like to keep the vertical center of the cubes where they are, but have the interior and exterior faces slant inwards.

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Sure. You could inset the faces with i and then delete the edge loops:

enter image description here

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Instead of extruding the the top faces of the base structure in your first image, simply hit I to inset the faces and while using the Inset tool, hold Ctrl to change the Depth (as it is called in the tool), which basically lets you move the inset faces up and down. While holding Ctrl you can change the height, when you release the key you can continue adjusting the inset width. When you've finished just left-click to confirm.

inset and depth

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