In mathematics
75 is a self number because there is no integer that added up to its own digits adds up to 75. [1] It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number, as well as a nonagonal number. [2] [3]
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... [4]
75 is the count of the number of weak orderings on a set of four items. [5]
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.
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