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 A133682 Number of regular complex polytopes in n-dimensional unitary complex space. 0
 1, 22, 8, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. REFERENCES 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. LINKS EXAMPLE 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. CROSSREFS Cf. A060296. Sequence in context: A159990 A243629 A040466 * A134911 A298145 A298176 Adjacent sequences:  A133679 A133680 A133681 * A133683 A133684 A133685 KEYWORD nonn AUTHOR Brian Hopkins, Jan 03 2008 STATUS approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)