Centered icosahedral number

Template:Short description Template:Infobox integer sequence In mathematics, the centered icosahedral numbers also known as cuboctahedral numbers are a sequence of numbers, describing two different representations for these numbers as three-dimensional figurate numbers. As centered icosahedral numbers, they are centered numbers representing points arranged in the shape of a regular icosahedron. As cuboctahedral numbers, they represent points arranged in the shape of a cuboctahedron, and are a magic number for the face-centered cubic lattice. The centered icosahedral number for a specific $n$ is given by $$\frac{(2n+1)(5n^2+5n+3)}{3}.$$

The first such numbers are

References

• Template:Cite OEIS.