171 (number)

171 (one hundred [and] seventy-one) is the natural number following 170 and preceding 172.

In mathematics
171 is a 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 $$\mathbb {M}$$ is defined as having cyclic groups ⟨ $$m$$ ⟩ that are linked with the function,
 * $$f_{m}(\tau) = q^{-1} + a_{1}q + a_{2}q^{2} + ..., \text{ } a_{k}$$ ∈ $$\mathbb{Z}, \text{ } q = e^{2\pi i \tau}, \text{ } \tau>0;$$ where $$q$$ is the character of $$\mathbb {M}$$ at $$m$$.

This generates 171 moonshine groups within $$\mathbb {M}$$ associated with $$f_{m}$$ that are principal moduli for different genus zero congruence groups commensurable with the projective linear group $$\operatorname{PSL_2}(\mathbb{Z})$$.