Chamfering is the process of cutting away or truncating edges of a polyhedron replacing sharp edges with new flat hexagonal faces. When applied to a cube, this operation transforms the original shape with 8 vertices into a new shape with 32 vertices - three new vertices at each corner. When the chamfer is increased and completely removes the original cube faces the resulting shape is a rhombic dodecahedron, a Catalan Solid with 14 rhombic faces.