Very popular during the Renaissance, this polyhedron is composed with n rings of 2n faces.
Inscribe a regular 2ngon in an "equatorial circle", then inscribe 2ngons in n "meridian circles" using as vertices the two poles and two of the preceding points (opposite on the "equatorcircle"). To complete the polyhedron connect the vertices of these n polygons with lines parallel to the equator. For n=2 you get the regular octahedron. 

Just for the fun, here is an approximation of an oblate spheroid (ellipsoid with two axis of same length, and the "polar axis" smaller). Our earth looks like this polyhedron, but it is much nicer! 
These polyhedra are constructed starting from Plato's polyhedra; a tessellation is drawn on each face and the central projection on the circumsphere defines the new vertices. Fuller widely popularized the structures based on this concept. Here are three examples constructed from the regular octahedron (triangulation in 9), dodecahedron (triangulation in 5) and icosahedron (triangulation in 4).
8x9=72 faces 
12x5=60 faces 
20x4=80 faces 
S_{15} : 26 faces, symmetry group C_{3}

S_{16} : 24+2 faces, symmetry group C_{4v}

an other S_{16} : 28 faces, symmetry group T

references: 
The Penguin dictionary of curious and interesting geometry by David Wells (Penguin Books, 1991).
Polyhedra (pages 106107) by Peter R. Cromwell (Cambridge University Press, 1997). Martin's Pretty Polyhedra and the Repulsion Polyhedra Generator by Bob Allanson. Distributing Points on a Sphere by Paul Bourke. a polyhedral celestial globe to be realize by yourself 
summary  March 2004 updated 08072005 