Observations on Haüy Rhombic Dodecahedral Numbers with Some Special Numbers

In this paper, the basic definition of Haüy rhombic dodecahedral numbers and nasty numbers are given. The Haüy rhombic dodecahedral number is taken into study and we prove this number is a combination of some special numbers. Also, we investigate about the relationships between the Haüy rhombic dodecahedral, stella octangula, hex number, centered tetrahedral and gnomonic numbers. For the clear understanding of the properties of special numbers we proved fifteen theorems. Sixteen special numbers are taken into consideration for this observation. The key points are given in the proof of the theorems.