Well, here is the D-Type Schwartzite with all heptagons in blue. It is easy to see that there is a three-fold rotational symmetry axis along each pod. Totally, there are 3x4=12 heptagons in a unit cell.
This structure is similar to the molecular tetrapod I posted before. However, there are some restrictions due to the patching condition between the tube and endcaps for the same reason as the situation in the endcapped nanotubes. For instance, the tetrapod I made has larger girths.