The coordinates of the vertices of the polyhedron are expressed in terms of the acute angle of the rhombus. If you vary this angle from 0° to 90°, then 30 of the rhombi are deformed to a cube and the rest are deformed to a rectangle. (At both extremes the cubes and rectangles come from the same rhombi.)

The Euler characteristic of is . Consequently, its genus , which means that it is topologically equivalent to a doughnut with 11 holes, or, if you prefer, to a sphere with 11 handles.