>>11920784I am going to say no. Here's why.
We'll restrict it to 3d but is should be valid for all dimensions.
If I take a 3 dimensional non-uniformly shaped object and put a point at its center, then form a sphere around it equidistant from its center, then project the image of the outline of the shape on to a tangent plane at every point on the sphere, the point will not be at the center of every projection onto the tangent plane to the sphere.
This means that there are centers of the outer surface as seen by the frame made by the tangent plane of the equidistant sphere that are not going to line up with the center of the shape.
I'm just eyeballing that because the olive suspended by a toothpick in the center of my tumbler of gin is not always at the center of the outline of the glass I can see while lying on the floor.
