A dissection of quarter of rhombic dodecahedron of the second kind to a cube

Izidor Hafner Tomislav Zitko Faculty of Electrical Engineering, University of Ljubljana Trzaska 25 , 1000 Ljubljana , Slovenia e-mail: izidor.hafner@fe.uni-lj.si

In [1] we found a symmetric dissection of 2 rhombic dodecahedra of the second kind (RD2) to a cube. The dissection uses 25 pieces and is based on space filling by rhombic dodecahedra of the second kind. Computation shows that the side length of the cube is identical to the length of the longer diagonal of the rhombus. In this article we simplify the construction by showing that a quarter of RD2 can be dissected to four pieces to get a small cube. Two RD2s can give 8 small cubes which form a larger cube. To see a (LiveGraphics3D) animation double click the picture.

To make a paper model of a cube, use the following nets. Two of the nets should be folded in the opposite direction to make the mirror image of a solid.

References

[1] I. Hafner, T. Zitko, A dissection of two rhombic dodecahedra of the second kind to a cube.