We describe the smallest C-groups with complete diagram whose rank 3 residues are hypermaps of type (n,n,n). It turns out that these C-groups are not hypertopes, indeed all rank 3 residues fail to be thin. We then focus on rank 3 regular hypertopes. A characterization of thiness will be given and some infinite families of ``small'' rank 3 regular hypertopes of type (n,n,n) will arise.