•A novel family of cage molecules, the porous carbon nitride fullerenes (PCNFs) is proposed and studied thoretically.[1] •They are the 0-D counterparts of 2D graphitic carbon nitrides [2-6], in analogy with icosahedral fullerene, being the 0D counterpart of graphene. •We study two members of the PCNF family, the icosahedral C60N60 and C120N60. •We demonstrate their electronic, vibrational, and thermal stability. •Their revealed properties are promising for several applications.