90 (number)

90 is a pronic number, as it is the product of 9 and 10.[1] It is nontotient[2] and divisible by the sum of its decimal digits, making it a Harshad number.[3]

• It is the third unitary perfect number, since it is the sum of its unitary divisors excluding itself,[4] and because it is equal to the sum of a subset of its divisors, it is also a semiperfect number.[5]

• 90 is a Stirling number of the second kind ${\displaystyle S(n,k)}$ from a ${\displaystyle n}$ of ${\displaystyle 6}$ and a ${\displaystyle k}$ of ${\displaystyle 3}$, as it is the number of ways of dividing a set of six objects into three non empty subsets.[6]

• It is a Perrin number from a sum of 39 and 51, which average 45, the ninth triangular number or sum of the first nine non-zero positive integers.[7][8]

• 90 is the fifth sum of non-triangular numbers, respectively between the fifth and sixth triangular numbers, 15 and 21 (equivalently 16 + 17 ... + 20).[9]

In normal space, the interior angles of a rectangle measure 90 degrees each. Also, in a right triangle, the angle opposing the hypotenuse measures 90 degrees, with the other two angles adding up to 90 for a total of 180 degrees.[10] Thus, an angle measuring 90 degrees is called a right angle.[11]

The truncated dodecahedron and truncated icosahedron both have 90 edges. A further four uniform star polyhedra (U₃₇, U₅₅, U₅₈, U₆₆) and four uniform compound polyhedra (UC₃₂, UC₃₄, UC₃₆, UC₅₅) contain 90 edges or vertices.

The rhombic enneacontahedron is a zonohedron with a total of 90 rhombic faces: 60 broad rhombi akin to those in the rhombic dodecahedron with diagonals in ${\displaystyle 1:{\sqrt {2}}}$ ratio, and another 30 slim rhombi with diagonals in ${\displaystyle 1:\varphi ^{2}}$ golden ratio. The obtuse angle of the broad rhombic faces is also the dihedral angle of a regular icosahedron, with the obtuse angle in the faces of golden rhombi equal to the dihedral angle of a regular octahedron and the tetrahedral vertex-center-vertex angle, which is also the angle between Plateau borders: ${\displaystyle 109.471}$°. The rhombic enneacontahedron is the zonohedrification of the regular dodecahedron, and it is the dual polyhedron to the rectified truncated icosahedron, a near-miss Johnson solid. On the other hand, the final stellation of the icosahedron has 90 edges. It also has 92 vertices like the rhombic enneacontahedron, when interpreted as a simple polyhedron.

The Witting polytope contains ninety van Oss polytopes such that sections by the common plane of two non-orthogonal hyperplanes of symmetry passing through the center yield complex Möbius–Kantor polygons.[12] The root vectors of simple Lie group E₈ are represented by the vertex arrangement of the 4₂₁ polytope, which is shared by the Witting polytope in four-dimensional complex space.

Ninety is:

• the atomic number of thorium, an actinide. As an atomic weight, 90 identifies an isotope of strontium, a by-product of nuclear reactions including fallout. It contaminates milk.
• the latitude in degrees of the North and the South geographical poles.

• Nike Total 90 Apparel is a brand name of football apparel and football equipment from equipment bags to goalkeeper gloves
• Major League Baseball bases are 90 feet (27 m) apart.
• The car number most associated with former NASCAR team owner Junie Donlavey
• The total number of minutes in an association football match.

Interstate 90 is a freeway that runs from Washington to Massachusetts.

• +90 is the code for international direct dial phone calls to Turkey.
• 90 is the code for the French département Belfort.
• Interstate 90 is a major east-west controlled access highway that spans the continental United States for 3,020 miles (4,860 kilometers) from Seattle to Boston.