75 (number)
Template:Infobox number 75 (seventy-five) is the natural number following 74 and preceding 76.
In mathematicsEdit
75 is a self number because there is no integer that added up to its own digits adds up to 75.<ref>Template:Cite OEIS</ref> It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number, as well as a nonagonal number.<ref>Template:Cite OEIS</ref><ref>Template:Cite OEIS</ref>
It is also the fourth ordered Bell number, and a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7, 5, 12, 17, 29, 46, 75...<ref>Template:Cite OEIS</ref>
75 is the count of the number of weak orderings on a set of four items.<ref>Template:Cite OEIS</ref>
Excluding the infinite sets, there are 75 uniform polyhedra in the third dimension, which incorporate star polyhedra as well. Inclusive of 7 families of prisms and antiprisms, there are also 75 uniform compound polyhedra.