In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, 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 ancient Greek mathemat ...
that represents a
dodecahedron
In geometry, a dodecahedron (; ) or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three Kepler–Po ...
. The centered dodecahedral number for a specific ''n'' is given by
:
The first such numbers are:
1,
33,
155
Year 155 ( CLV) was a common year starting on Tuesday of the Julian calendar. At the time, it was known as the Year of the Consulship of Severus and Rufinus (or, less frequently, year 908 ''Ab urbe condita''). The denomination 155 for this year ...
, 427, 909, 1661, 2743, 4215, 6137, 8569, … .
Congruence Relations
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*
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{{Num-stub
Figurate numbers