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A111336 Number of convex regular polytopes with n hyperfaces. 1
1, 2, 2, 3, 2, 4, 2, 3, 2, 4, 2, 3, 2, 4, 2, 3, 2, 4, 2, 3, 2, 4, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

COMMENTS

The minimum number of hyperfaces required for a convex polytope is 3, and the only convex polytope with 3 hyperfaces is a triangle. - Jianing Song, Sep 17 2018

LINKS

Table of n, a(n) for n=3..89.

Wikipedia, Elenco di politopi regolari.

Wikipedia, Regular Polytopes.

FORMULA

a(3) = 1; a(n) = 2 if n = 4 or n is odd and >= 5; a(n) = 4 if n = 12, 20, 24, 120, 600 or a power of 2 >= 8; a(n) = 3 otherwise. - Jianing Song, Sep 17 2018

EXAMPLE

a(8) = 4 because the regular polytopes with 8 faces are the octagon, the octahedron, the four-dimensional cube and the 7-dimensional simplex.

PROG

(PARI)

a(n)={

    if(n==3, return(1));

    if(n==4||(n>=5&&n%2==1), return(2));

    if(n>=6&&n%2==0, return(3+(n==12||n==20||n==24||n==120||n==600||(n>=8&&omega(2*n)==1))));

    else(return(0));

}} \\ Jianing Song, Sep 17 2018

CROSSREFS

Cf. A302139 (indices of 4).

Sequence in context: A274517 A038148 A141829 * A083902 A205562 A217984

Adjacent sequences:  A111333 A111334 A111335 * A111337 A111338 A111339

KEYWORD

nonn,easy

AUTHOR

Paulo de A. Sachs (sachs6(AT)yahoo.de), Nov 09 2005

EXTENSIONS

Terms beyond a(38) from Jianing Song, Sep 17 2018

STATUS

approved

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Last modified September 15 22:10 EDT 2019. Contains 327088 sequences. (Running on oeis4.)