="Bill Gosper" <billgosper@gmail.com> We could recognize the (countable) family of "M" antiprisms and call this the pentagonal one. Better name: pentiprisms--like antiprisms but with equilateral pentagons instead of equilateral triangles. Alternatively, see below. MLB>Heh, I see the faces as W's. Curious: are there analogs with concave nonagons, or anything like that? I doubt it. See gosper.org/pentiprisms.png for orders 3 thru 8 concave and convex. I think Julian (but maybe NeilB) found the extra (squat) hexagonal one. I find no more. --rwg I think all the Google hits on pentiprism are misspellings of pentaprism. Other naming scheme: We could regard the regular dodecahedron as a polar-truncated pentagonal trapezohedron, and similarly for the other figures in the bottom two rows. And we could call Julian's solid a polar-overtruncated pentagonal trapezohedron, etc. for the top row. Unfortunately, this is how to make, rather than how they look. Few people can visualize, let alone recognize, the result of the truncation planes passing through each other, extending faces instead of shortening them.