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I have the following object:

enter image description here

How do I modify the origin so that the origin has the X axis normal to the face shown, but the object itself remains in the same position in space?

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Because you've applied the rotation to your model, the easiest possible way to do this is rotating it manually.

Turn on the snapping tool by using the magnet icon in the bottom toolbar and set the snap element to Increment.

Enter top view by pressing Numpad 7, then enter Orthographic Mode by pressing Numpad 5. Use the keys G,Z to rotate along the Z axis and hold Shift until the flat faces facing the x axis are exact straight lines.

While still in object mode, use Ctrl+A and click Rotation to reset the rotation to 0,0,0.

With Pictures:

enter image description here enter image description here enter image description here

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I dont know if i get the question correctly but maybe it helps you to go into object mode, open N menu and check the rotation in the transform tab (first tab). Hope that is what youre looking for

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  • $\begingroup$ The OP asks how to align the origin to a face, which implies changing the relative orientation between the object local axes and the object vertices. Setting the object global rotation to 0 won't do that as everything will be rotated at once, local origin and vertices. $\endgroup$ – mins Aug 4 '18 at 14:56

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