The centered polyhedral numbers are a class of
figurate number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean
* polyg ...
s, each formed by a central dot, surrounded by
polyhedral layers with a constant number of edges. The length of the edges increases by one in each additional layer.
Examples
*
Centered tetrahedral numbers
*
Centered cube number
A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with points on the square faces of the th layer. Equival ...
s
*
Centered octahedral number
A centered octahedral number or Haüy octahedral number is a figurate number that counts the number of points of a three-dimensional integer lattice that lie inside an octahedron centered at the origin. The same numbers are special cases of t ...
s
*
Centered dodecahedral numbers
*
Centered icosahedral numbers
*
Stella octangula number
In mathematics, a stella octangula number is a figurate number based on the stella octangula, of the form ..
The sequence of stella octangula numbers is
:0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, ...
Only two of these numbers are squar ...
s
References
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{{Num-stub
Figurate numbers