Retaining ring having inner surfaces with features

A retaining ring comprising:

• an annular body including
• a top surface configured to be secured to a carrier head;
• a bottom surface configured to contact a polishing surface;
• an outer surface extending from the top surface at an outer top perimeter to the bottom surface at an outer bottom perimeter;
• and
• an inner surface extending from the top surface at an inner top perimeter to the bottom surface at an inner bottom perimeter, the inner surface comprising a first portion adjacent the bottom surface and a second portion adjoining the first portion along a boundary, wherein the first portion of the inner surface comprises seven or more planar facets, adjacent planar facets of the first portion of the inner surface being connected at a straight side edge, and the inner bottom perimeter defined by straight bottom edges of the planar facets, and wherein the second portion comprises a frustoconical surface that is sloped downwardly from outside in.