171 (number) explained
| Number: | 171 |
| Divisor: | 1, 3, 9, 19, 57, 171 |
171 (one hundred [and] seventy-one) is the natural number following 170 and preceding 172.
In mathematics
171 is the 18th triangular number and a Jacobsthal number.
There are 171 transitive relations on three labeled elements, and 171 combinatorially distinct ways of subdividing a cuboid by flat cuts into a mesh of tetrahedra, without adding extra vertices.[1]
The diagonals of a regular decagon meet at 171 points, including both crossings and the vertices of the decagon.
There are 171 faces and edges in the 57-cell, an abstract 4-polytope with hemi-dodecahedral cells that is its own dual polytope.[2]
is defined as having
cyclic groups ⟨
⟩ that are linked with the function,
fm(\tau)=q-1+a1q+a2q2+...,ak
∈
where
is the
character of
at
.This generates 171
moonshine groups within
associated with
that are
principal moduli for different
genus zero congruence groups
commensurable with the
projective linear group
.
[3] See also
Notes and References
- Pellerin . Jeanne . Verhetsel . Kilian . Remacle . Jean-François . 1801.01288 . December 2018 . 10.1145/3272127.3275037 . 6 . ACM Transactions on Graphics . 1–9 . There are 174 subdivisions of the hexahedron into tetrahedra . 37. 54136193 .
- Book: McMullen . Peter . Peter McMullen . Schulte . Egon . Egon Schulte . 10.1017/CBO9780511546686 . 0-521-81496-0 . 1965665 . 185–186, 502 . Cambridge University Press . Cambridge . Encyclopedia of Mathematics and its Applications . Abstract Regular Polytopes . 92 . 2002 . 115688843 .
- Conway . John . John Horton Conway . Mckay . John . John McKay (mathematician) . Sebbar . Abdellah . On the Discrete Groups of Moonshine . Proceedings of the American Mathematical Society . 132 . 8 . 2004 . 2233 . 10.1090/S0002-9939-04-07421-0 . free . 1088-6826 . 4097448 . 54828343 .
