171 (number)

Template:Infobox number 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.

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.

Within moonshine theory of sporadic groups, the friendly giant $𝕄$ is defined as having cyclic groups ⟨ $m$ ⟩ that are linked with the function,

$f_m(\tau )=q^{-1}+a_{1}q+a_2{q}^2+...,a_k$ ∈ $\mathbb{Z},q=e^{2\pi i\tau },\tau >0;$ where $q$ is the character of $𝕄$ at $m$.

This generates 171 moonshine groups within $𝕄$ associated with $f_m$ that are principal moduli for different genus zero congruence groups commensurable with the projective linear group $\mathrm{P}\mathrm{S}{\mathrm{L}}_{\mathrm{2}}(\mathbb{Z})$.

See also

• Template:In title