A060296 Number of regular convex polytopes in n-dimensional space, or -1 if the number is infinite.

1, 1, -1, 5, 6, 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, 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: 0

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Mar 24 2001

Keywords

• sign
• easy

Examples

			a(2) = -1 because of the regular polygons in the plane.
a(3) = 5 because in R^3 the regular convex polytopes are the 5 Platonic solids.
		

References

• H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973.
• B. Grünbaum, Convex Polytopes. Wiley, NY, 1967, p. 424.
• P. McMullen and E. Schulte, Abstract Regular Polytopes, Encyclopedia of Mathematics and its Applications, Vol. 92, Cambridge University Press, Cambridge, 2002.

Links

• John Baez, Platonic Solids in All Dimensions, Nov 12 2006.
• Brady Haran, Pete McPartlan, and Carlo Sequin, Perfect Shapes in Higher Dimensions, Numberphile video (2016)
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A000943, A000944, A053016, A063927, A093478, A093479.

Programs

Mathematica

PadRight[{1, 1, -1, 5, 6}, 100, 3] (* Paolo Xausa, Jan 29 2025 *)

Formula

a(n) = 3 for all n > 4. - Christian Schroeder, Nov 16 2015