mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, 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 ancient Greek mathemat ...

s, each formed by a central dot, surrounded by

polyhedral In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary surfa ...

layers with a constant number of edges. The length of the edges increases by one in each additional layer.

Examples

Centered tetrahedral number In mathematics, a centered tetrahedral number is a centered figurate number that represents a tetrahedron In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangul ...

s *

Centered cube number A centered cube number is a centered figurate number that counts the 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. Equivalently, it ...

s *

Centered octahedral number In mathematics, a centered octahedral number or Haüy octahedral number is a figurate number that counts the points of a three-dimensional integer lattice that lie inside an octahedron centered at the origin. The same numbers are special cases ...

s * Centered dodecahedral numbers * Centered icosahedral numbers * Stella octangula numbers

References

* {{Num-stub Figurate numbers