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A359367
a(n) = number of regular polytopes of rank m-n with group S_m, up to isomorphism and duality (this is independent of m if m >= 2n+3).
0
1, 1, 7, 9, 35, 48, 135
OFFSET
1,3
COMMENTS
Also known as string C-groups for S_m.
LINKS
Peter J. Cameron, Maria Elisa Fernandes and Dimitri Leemans, The number of string C-groups of high rank, arXiv:2212.12723 [math.GR], 2022.
EXAMPLE
a(1)=1 since the only regular polytope of rank m-1 with group S_m is the simplex.
CROSSREFS
Sequence in context: A177030 A189974 A316184 * A321760 A083203 A082536
KEYWORD
nonn,hard,more
AUTHOR
Peter J. Cameron, Dec 28 2022
EXTENSIONS
a(7) from Peter J. Cameron, Jan 19 2023
STATUS
approved