This model is a truncated octahedron that has
triangular cupolaic excavations in four of the hexagonal faces, and is then
drilled by a central octahedron to create a hole through the model. It has a
genus of 3.
Here's the shape of the hole, inside a transparent truncated octahedron.
An octahedron in the middle (red) with 4 faces augmented by
triangular cupolae (green).