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I am hoping to get some assistance in something I need for a project.

I am needing the cube here in the photos to actually take a fairly accurate impression of that face into the cube.

for my images attached, I have created a cube that has been subdivided a bunch of times in EDIT MODE

I have simply moved the most center vertices with proportional editing enabled to make my 2nd image, but getting accurate face impression manually would take too much time and would like to know if there is a modifier that can be used then finally applied to make it stay like it?

Many Thanks

Face1

Face2

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    $\begingroup$ I'd try some cloth simulation for this. or just copy th part of the face to the box mesh, and use a shapekey for animation it back to flat surface (if it is an animation). $\endgroup$ – Mechanic Jan 2 '19 at 4:35
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    $\begingroup$ Shrinkwrap modifier is exactly what you're looking for, use the project option $\endgroup$ – Dr. Farquaad Jan 2 '19 at 17:02
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In front ortho view bake a displacement map of the face and apply it later to the subdivided plane. Later extrude the edges of the plane and make a face to close it.

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Try changing the snapping element to face, and then in edit mode move the object towards the face object.

Snap Element

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