OFFSET
1,3
COMMENTS
For n > 8, the Coxeter groups are exactly A(n), B(n) = C(n), and D(n), hence a(n) = 3.
REFERENCES
H. S. M. Coxeter, Regular Polytopes, Dover Publications, Inc., 1973.
LINKS
FORMULA
G.f.: (1 - 2*x + 4*x^2 + 2*x^3 - 2*x^4 + x^5 - x^8)/(1 - x). - Stefano Spezia, Jul 15 2024
EXAMPLE
For n = 4, there are five finite groups, denoted A(4) (symmetry group of the simplex), B(4) (= C(4)) (symmetry group of the tesseract and the 4-dimensional cross polytope), D(4) (symmetry group of the demitesseract), F(4) (symmetry group of the 24-cell) and H(4) (symmetry group of the 120-cell and the 600-cell).
PROG
(PARI) a(n)=if(n>8, 3, [1, -1, 3, 5, 3, 4, 4, 4][n]) \\ Charles R Greathouse IV, Jul 15 2024
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Douglas Boffey, Jul 14 2024
STATUS
approved