Cube Drilled by Triangular Prism
This Demonstration shows a cube pierced by a triangular prism whose edges are parallel to a diagonal of the cube.
In [1, p. 326], the solid is described as a toroid with nine faces of two kinds.
 L. Szilassi, "On Three Classes of Regular Toroids," Symmetry: Culture and Science, 11(1-4), 2000 pp. 317–335.