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Rhombic Dodecahedral Number

A Figurate Number which is constructed as a centered Cube with a Square Pyramid appended to each face,

{\it RhoDod}_n={\it CCub}_n+6P_{n-1}=(2n-1)(2n^2-2n+1),

where ${\it CCub}_n$ is a Centered Cube Number and $P_n$ is a Pyramidal Number. The first few are 1, 15, 65, 175, 369, 671, ... (Sloane's A005917). The Generating Function of the rhombic dodecahedral numbers is


See also Octahedral Number


Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 53-54, 1996.

Sloane, N. J. A. Sequence A005917/M4968 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein