LetP ^d be ad-polytope and letN (P) be the set of outward normal vectors to its facets.P is said to be primitive if it has the property that there exists no polytopeQ withN(Q) N(P). In other words, removal of any facet ofP leaves an unbounded polyhedral set. The primitive polytopes withd+1 facets and with 2d facets are well known (they are the simplices and the parallelotopes), the primitive polytopes withd+2 and 2d–1 facets have also been classified. The present paper deals with primitive polytopes with 2d–2 facets.