1,2

In each dimension there are infinite families which we count as a single polytope: the generalized complex n-cube with generalized Schlaefli symbol m(4)2(3)2...2(3)2 with m^n vertices, and its dual, the generalized complex n-cross-polytope.

H. S. M. Coxeter, Regular complex polytopes, Cambridge University Press, 1974.

E. Schulte, Symmetry of Polytopes and Polyhedra, in J. E. Goodman and J. O'Rourke, Handbook of discrete and computational geometry, 2nd edition, Chapman & Hall / CRC, 2004.

G. C. Shepherd, Regular complex polytopes, Proc. Lond. Math. Soc. (3), Vol. 2 (1952), pp. 82 - 97.

a(3) = 8 because in C^3 the regular complex polytopes correspond to the following generalized Schlaefli symbols: m(4)2(3)2 (generalized complex cube), 2(3)2(4)m (generalized complex octahedron), 2(6)2(6)2 (tetrahedron), 2(6)2(10)2 (icosahedron), 2(10)2(6)2 (dodecahedron), 3(3)3(3)3, 3(3)3(4)2, 2(4)2(3)3.

Cf. A060296.

Sequence in context: A040467 A069285 A040466 this_sequence A134911 A113783 A058402

Adjacent sequences: A133679 A133680 A133681 this_sequence A133683 A133684 A133685

nonn

Brian Hopkins (bhopkins(AT)spc.edu), Jan 03 2008