Excavated truncated rhombicuboctahedron

The excavated truncated rhombicuboctahedron is a quasi-convex Stewart toroid. It can be obtained by excavating 12 unit-edge-length irregular octagonal prisms from a truncated rhombicuboctahedron, then excavating the central polyhedron as well (blending it with the remaining irregular-octagon faces of the prisms and opening up that space). Since the irregular faces are all blended away, the toroid is regular-faced. Its convex hull is an equilateral truncated rhombicuboctahedron, with 6 regular octagons, 12 rectangular-symmetric octagons, 8 hexagons, and 24 squares.

The central polyhedron is a truncation of the rhombic dodecahedron that cuts away both types of vertices, with 6 squares, 8 triangles, and 12 rectangular-symmetric octagons.

The excavated truncated rhombicuboctahedron can also be obtained by outer-blending six square cupolae, eight triangular cupolae, and twenty-four triangular prisms together.

Related polyhedra
If the cupolae are "contracted" into pyramids (by removing the side squares and pulling the side triangle faces together, like the opposite of a partial expansion), an excavated expanded cuboctahedron will be formed.

If the triangular prisms are removed (and the cupolae brought together), a truncated cuboctahedron excavated with cubes and a central small rhombicuboctahedron will be formed.