Space filling with rhombic dodecahedra and prolate rhombohedra

Izidor Hafner, Faculty of Electrical Engineering, University of Ljubljana

Eight prolate rhombohedra with common vertex form a cube. Space between them can be filled by six rhombic dodecahedra. The volume of the cube equals the volume of these solids. Cubes fill the space. We can take six rhombic dodecahedra of the second kind and eight prolate rhombohedra to form a prototile that fill the space as well.