Centered icosahedral number
Total no. of terms | Infinity |
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Subsequence of | Polyhedral numbers |
Formula | |
First terms | 1, 13, 55, 147, 309, 561, 923 |
OEIS index |
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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
- Sloane, N. J. A. (ed.). "Sequence A005902 (Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
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Figurate numbers
centered |
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non-centered |
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centered |
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non-centered | |
pyramidal |
non-centered |
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non-centered |
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