As far as I can understand it, the vaulting upto the level of the lantern is stone; above that everything is timber. There must be some substantial ironwork at the transition.

"The timber lantern was designed by William Hurley, the King's carpenter. It is framed by eight vertical oak posts 63ft high, each weighing 10 tons. .. positioned on the stone base. The posts are braced by a complex framework of timber struts and curved members with a compression ring at the top, vaulted in timber above". See http://www.panoramio.com/photo/5877782 for the timber, but let me know if you find better. There are tours up there on offer, but you have to check in for a particular day