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This paper studies the convex hull of n random points in Rd. A recently-proved topological identity of the author is used in combination with identities of Efron and Buchta to flnd the expected number of vertices of the convex hull { yielding a new recurrence formula for all dimensions d. A recurrence for the expected number of facets and (d¡2)-faces is also found, this analysis building on a technique of Renyi and Sulanke. Other relationships for the expected count of i-faces (1 • i < d) are found when d • 5, by applying the Dehn{Sommerville identities. A general recurrence identity (see equation (3) below) for this expected count is conjectured. Published version: This is the personal-archive version of the paper which is published in the journal Discrete and Computational Geometry, 2008. The original publication is available at www.springerlink.com. The Springer DOI is: 10.1007/s00454-008-9122-6.

Recurrence Relationships for the Mean Number of Faces and Vertices for Random Convex Hulls