171 (one hundred
ndseventy-one) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
following
170 and preceding
172
Year 172 ( CLXXII) was a leap year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Scipio and Maximus (or, less frequently, year 925 '' Ab urbe condita ...
.
In mathematics
171 is a
triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...
and a
Jacobsthal number In mathematics, the Jacobsthal numbers are an integer sequence named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers, they are a specific type of Lucas sequence U_n(P,Q) for which ''P'' = 1, and ''Q''& ...
.
There are 171
transitive relation
In mathematics, a relation on a set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Each partial order as well as each equivalence relation needs to be transitive.
Definition
A homog ...
s on three labeled elements, and 171 combinatorially distinct ways of subdividing a
cuboid
In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the length of the edges or the angles between edges and faces a cuboid can be transformed into a cub ...
by flat cuts into a mesh of
tetrahedra
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
, without adding extra vertices.
The diagonals of a regular
decagon
In geometry, a decagon (from the Greek δέκα ''déka'' and γωνία ''gonía,'' "ten angles") is a ten-sided polygon or 10-gon.. The total sum of the interior angles of a simple decagon is 1440°.
A self-intersecting ''regular decagon'' i ...
meet at 171 points, including both crossings and the vertices of the decagon.
There are 171
faces
The face is the front of an animal's head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affe ...
and
edges in the
57-cell, an
abstract 4-polytope with hemi-
dodecahedral
In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon ...
cells that is its own
dual polytope
In geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other ...
.
See also
* The year AD
171
Year 171 (Roman numerals, CLXXI) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Severus and Herennianus (or, less frequently, year 92 ...
or 171 BC
*
List of highways numbered 171
*
References
{{DEFAULTSORT:171 (Number)
Integers