A special case of mahler’s conjecture

A special case of Mahler's conjecture on the volume-product of symmetric convex bodies in n -dimensional Euclidean space is treated here. This is the case of polytopes with at most 2n+2 vertices (or facets). Mahler's conjecture is proved in this case for n≤ 8 and the minimal bodies are characterized. <lsiheader> <onlinepub>7 August, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; <pdfname>20n2p163.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>no <sectionname> </lsiheader> Received May 28, 1996, and in revised form November 7, 1996.