This form of vase, typically called navette or nef, is of a model produced in the 17th Century after a design by the abbé Elpidio Benedetti (c.1610-1690). Benedetti was the Roman agent of Cardinal Mazarin and, upon the latter's death in 1661 became that of Louis XIV.
Benedetti's designs for a closely related navette vase and other examples, entitled 'Desseins de sept vazes de différentes formes de l'abbé Benedetti', are now in the Cabinet des Estampes at the Bibliothèque Nationale de France, Paris (ill. in P. Malgouyres, Porphyre, la Pierre Pourpre des Ptolémées aux Bonaparte, Paris, 2003, p.138, fig.65, see in particular fig. C). Benedetti was the Roman agent of Cardinal Mazarin and, upon the latter's death in 1661 became that of Louis XIV.
Closely related examples at Versailles include a virtually identical covered porphyry vase - albeit devoid of any mounts - in the Galerie des Glaces at Versailles which rests on a Louis XIV giltwood centre table carved with the cipher of the Duc d'Antin (ill. in P.Arizzoli-Clémentel, Versailles, Furniture of the Royal Palace, 17th and 18th Centuries, vol. 2, Dijon, 2002, pp.171 and 173, no.56, and again in P.Arizzoli-Clémentel, La Galerie des Glaces, Dijon, 2007, p.95) and reproduced here.
Interestingly, P. Malgouyres discusses how the abbé Benedetti typically prepared designs for the furniture, upholstery and statues which he intended to procure to his most important patrons, and how the design for the navette vase illustrated op.cit, fig. C was probably that used to produce the above-mentioned navette vase in the Galerie des Glaces.
Two further related examples of vases navette, albeit carved with handles, are in the Musée du Louvre (inv. OA9232 and 9233) and illustrated in P. Malgouyres, op.cit, p.113, no.26. Two further 'navettes à consoles' vases, each with ball finial, formerly in the collections of Louis XIV and recorded in the Galerie des Glaces in the inventory drawn in 1722, are now in the Louvre (OA9234 and OA9236), while the pair to one of these is at the château d'Ecouen (Ibid, p.115, figs 29 and 30).