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The thermoelectric properties of the three pyrite-type IIB-VIA2 dichalcogenides (ZnS2, CdS2 and CdSe2) are systematically investigated and compared with those of the prototype ZnSe2 in order to optimize their thermoelectric properties. Using the phonon Boltzmann transport equation, we find that they all have ultralow lattice thermal conductivities. By analyzing their vibrational properties, these are attributed to soft phonon modes derived from the loosely bound rattling-like metal atoms and to strong anharmonicities caused by the vibrations of all atoms perpendicular to the strongly bound nonmetallic dimers. Additionally, by correlating those properties along the series, we elucidate a number of chemical trends. We find that heavier atom masses, larger atomic displacement parameters and longer bond lengths between metal and nonmetal atoms can be beneficial to the looser rattling of the metal atoms and therefore lead to softer phonon modes, and that stronger nonmetallic dimer bonds can boost the anharmonicities, both leading to lower thermal conductivities. Furthermore, we find that all three compounds have complex energy isosurfaces at valence and conduction band edges that simultaneously allow for large density-of-states effective masses and small conductivity effective masses for both p-type and n-type carriers. Consequently, the calculated thermoelectric figures of merit (ZT), can reach large values both for p-type and n-type doping. Our study illustrates the effects of rattling-like metal atoms and localized nonmetallic dimers on the thermal transport properties and the importance of different carrier effective masses to electrical transport properties in these pyrite-type dichalcogenides, which can be used to predict and optimize the thermoelectric properties of other thermoelectric compounds in the future.