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If I have a shape key that extrudes the mesh upwards. then I want to make another shape key that will extrude the mesh(which is already extruded upwards) sideways, when I try to do so, only the original vertices can be edited not the new one created by the first keyframe. Does anyone know how to do that?

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Shape keys do not support operations that create new geometry. You can imagine them as just a list of vertex coordinates for each vertex that was present at the time the shape key was created. If you create new vertices by extruding, the shape key you made previously won't have any reference to those.

A solution to your problem is doing all the extruding first and then creating the two shape keys afterwards. Select the second shape key, go into edit mode and then move the part of the model you extruded sidewards back to its original position. With the second shape key set to 1, select the first shape key and 'undo' the movement of the first upwards extrusion. Now you have two shape keys that "extrude" your mesh, albeit with inverted values.

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    $\begingroup$ Note that in doing so, you need to think about how it will look while the fake extrusion shapekey is disabled: overlapping geometry might produce z-fighting issues. $\endgroup$
    – Lauloque
    Commented Aug 8, 2023 at 23:09

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