Английская Википедия:171 (number)

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Шаблон:Infobox 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 <math>\mathbb {M}</math> is defined as having cyclic groups ⟨ <math>m</math> ⟩ that are linked with the function,

<math>f_{m}(\tau) = q^{-1} + a_{1}q + a_{2}q^{2} + ... , \text{ } a_{k}</math> ∈ <math>\mathbb{Z}, \text{ } q = e^{2\pi i \tau}, \text{ } \tau>0;</math> where <math>q</math> is the character of <math>\mathbb {M}</math> at <math>m</math>.

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

See also

• The year AD 171 or 171 BC
• List of highways numbered 171
• Шаблон:In title