Rhodonite, an attractive pink and white gemstone, has a structure commonly called sugary: the material has small openings that will give an "orange-peel" surface that resembles badly polished jade. It is not the same thing, however. The orange-peel on jade comes from directional dissimilar hardness, or grain structure; the voids in rhodonite are actual holes and will not polish out. One could probably fill them with one of the epoxies that are used to stabilize turquoise but the epoxy won't polish as well as the rhodonite and the results I have seen were not satisfactory. "Superglue", or cyanoacrylate, works better, but treatments of this kind should always be disclosed to any purchaser.
I have been able to improve the polish (but not completely) using chrome oxide on hard leather I mix it with water, using a 5 to1 oxide to water ratio, then add about 10% Linde A, which is an aluminum oxide polishing compound commonly used on jade. Another option is to dry-sand on 1200 grit silicon carbide after sanding through 1200 using diamond, then polishing with straight aluminum oxide mixed with enough water to make a paste.
The best answer I know of is to find better material. Like most lapidary material, rhodonite comes in a wide range of quality and in the better grades the voids are small enough not to show after the final polish. Of course they still show under magnification, but most people don't care about things they can't see.
By Dick Friesen