How can I inset/extrude a face, so that the outer faces have the same width?
Any kind of help is appreciated
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You can use the
Inset Faces tool, which you can activate by pressing I. Do note that this won't work if the object was scaled in Object Mode.
You scaled your object in object mode. If you want to have the inset work properly, you will have to scale the plane or what ever you are starting with in edit mode, or apply the scale if done in object mode. When you scale in object mode you are making it “look” correct, but it won’t be correct unless your editing of shapes are done in edit mode or applied in object mode.
The top rectangle was scaled in the X direction in object mode without applying the transformation then the inset was added. The one on the bottom was scaled in the X direction in edit mode and then the inset was added. If you apply the scale in object mode to the top rectangle in object mode then do the inset, you will have the same result as the bottom one.
Remember, transformations in object mode are what you want it to look like, but transformations in edit mode (or that are applied using Ctrl-A menu in object mode) are what it is like.