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
Keywords
Examples
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.
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
- G. C. Shephard, Regular complex polytopes, Proc. Lond. Math. Soc. (3), Vol. 2 (1952), pp. 82-97.
Crossrefs
Cf. A060296.
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