Centered icosahedral number
Total no. of termsInfinity
Subsequence ofPolyhedral numbers
Formula
First terms1, 13, 55, 147, 309, 561, 923
OEIS index

The centered icosahedral numbers and cuboctahedral numbers are two different names for the same 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 is given by

The first such numbers are

1, 13, 55, 147, 309, 561, 923, 1415, 2057, 2869, 3871, 5083, 6525, 8217, ... (sequence A005902 in the OEIS).

References