Does space time fabric actually fold upon itself when warped by an object of mass? 3D not 2D?

IE. a two dimensional plane shows the curvature towards an object of mass. In 3D would this actually be folding in and onto itself (no axis or an infinite amount of axis in every conceivable direction). If so what does this distortion of space time create, and does it bend light around the distortion or into the... show more IE. a two dimensional plane shows the curvature towards an object of mass. In 3D would this actually be folding in and onto itself (no axis or an infinite amount of axis in every conceivable direction). If so what does this distortion of space time create, and does it bend light around the distortion or into the distortion?
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