How Can We Help?
You are here:
< Back
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..
2-dimensional |
| ||||||
---|---|---|---|---|---|---|---|
3-dimensional |
| ||||||
4-dimensional |
| ||||||
Higher dimensional |
|
Classes of natural numbers | |||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
Categories
-
Annuals36
-
Bulbs, Corms & Tubers41
-
Ferns27
-
Fruits3
-
Garden Plants23
-
Grasses26
-
Herb17
-
Insects1
-
Mammals1
-
Midwest Native Plants0
-
Northeast Native Plants112
-
Perennials123
-
Rose1
-
Shrubs47
-
Trees112
-
Tropical Plants53
-
Upland Birds5
-
Vines18
-
Viola Tricolor1
-
Water Gardening & Plants9
-
Waterfowl0
-
Wetland Birds0
-
Wetland Plants4
-
Wildbirds172
-
Wildflowers1
-
Woodland Plants29
Table of Contents
Recent Comments