A133682 Number of regular complex polytopes in n-dimensional unitary complex space.

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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

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.

Links

Table of n, a(n) for n=1..70.

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

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