Decomposition of the Rhombic Dodecahedron (red-cyan glasses)

Cube, Pyramid
The 12 faces of the rhombic dodecahedron are rhombs. It is possible to decompose the rhombic dodecahedron to an inner cube and six pyramids. If you move the upper vertices of the pyramids to the other side of the pyramids’ bases, the pyramids can enter the cube and fill it without holes or overlaps. That proves that the rhombic dodecahedron’s volume is twice the volume of its inner cube. Use the sliders to change the distance between the pyramids and the cube and to bring the pyramids’ upper vertices to the other side of the bases.