Properties and Applications
The octahedral numbers have a generating function
Sir Frederick Pollock conjectured in 1850 that every number is the sum of at most 7 octahedral numbers: see Pollock octahedral numbers conjecture.
In chemistry, octahedral numbers may be used to describe the numbers of atoms in octahedral clusters; in this context they are called magic numbers.
Read more about this topic: Octahedral Number
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“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)