A060296 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

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

Table of n, a(n) for n=0..112.

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).

FORMULA

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

EXAMPLE

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.

CROSSREFS

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