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).

1, 1, 7, 9, 35, 48, 135

Offset: 1

Author

Peter J. Cameron, Dec 28 2022

Keywords

• nonn
• hard
• more

Comments

Also known as string C-groups for S_m.

Examples

			a(1)=1 since the only regular polytope of rank m-1 with group S_m is the simplex.
		

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.
• Dimitri Leemans and Jessica Mulpas, Two gluing methods for string C-group representations of the symmetric groups, arXiv:2504.17535 [math.CO], 2025. See p. 14.

Extensions

a(7) from Peter J. Cameron, Jan 19 2023