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A060296 Number of regular convex polytopes in n-dimensional space, or -1 if the number is infinite. 10
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
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)
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
Sequence in context: A222466 A195448 A079267 * A114598 A272489 A259500
KEYWORD
sign,easy
AUTHOR
Ahmed Fares (ahmedfares(AT)my-deja.com), Mar 24 2001
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)