171 (number)

← 170 171 172 ⊟
← 170 171 172 173 174 175 176 177 178 179 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred seventy-one
Ordinal	171st (one hundred seventy-first)
Factorization	32 × 19
Divisors	1, 3, 9, 19, 57, 171
Greek numeral	ΡΟΑ´
Roman numeral	CLXXI
Binary	101010112
Ternary	201003
Senary	4436
Octal	2538
Duodecimal	12312
Hexadecimal	AB16

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 $\operatorname {PSL_{2}} (\mathbb {Z} )$.

See also

• The year AD 171 or 171 BC
• List of highways numbered 171
• All pages with titles containing 171