Gyrotunnelled truncated cube

The gyrotunnelled truncated cube is a quasi-convex Stewart toroid. It can be made as the outer-blend of 8 tetrahedra and 4 square cupolae, or it can be made by tunnelling 2 square cupolas and 1 cube from a truncated cube. There are two ways to do this excavation, resulting in two distinct quasi-convex Stewart toroids. The gyrotunnelled variant results in octagonal faces sharing edges with square faces, while in the orthotunnelled variant octagons only share edges with triangles and other octagons. Both varieties have the same symmetry, face counts, and volumes.