A centered dodecahedral number is a
centered 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 term can mean
* polygo ...
that represents a
dodecahedron
In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentag ...
. The centered dodecahedral number for a specific ''n'' is given by
:
The first such numbers are 1, 33, 155, 427, 909, 1661, 2743, 4215, 6137, 8569, … .
Congruence Relations
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{{Num-stub
Figurate numbers