Orthotunnelled truncated cube

The tunnelled truncated cube is a quasi-convex Stewart toroid. It can be made by excavating 2 square cupolas and 1 cube from a truncated cube. There are two ways to do this, resulting in two distinct quasi-convex Stewart toroids. In the Stewart notation they are $$T_4 / Q_4(P_4)Q_4$$ and $$T_4 / g \overline{Q_4(P_4)Q_4}$$. They have the same symmetry, face counts, and volumes, but in one octagonal faces meet square faces at an edge and in the other octagonal and square faces share no edges.