Morphological operators for binary and grayscale images are commonly used to eliminate noise, recognize contours or specific structures, and arrange shapes in image processing. Even though morphology has been substantially developed in square-pixel-based-image-processing (SIP), no effort has been made to construct morphological operators in hexagonal-pixel-based-image-processing (HIP) yet. In this paper, we transform basic SIP-domain-morphological operators such as dilation, erosion, closing, and opening into HIP-domain and compare their performance with their SIP counterparts, taking into account 65 similarity- dissimilarity metrics for binary and four metrics for grey-scale proposed so far in the literature. It is the first time to give the fundamental morphological operators in the HIP domain. The operators developed in this paper initiate the research about morphology in the HIP domain by successfully filling a significant gap by eliminating HIP's lack of basic operators.