# A dissection of rhombic triacontahedron

Izidor Hafner

Tomislav Zitko

Faculty of Electrical Engineering, University of Ljubljana

Trzaska 25
, 1000 Ljubljana
, Slovenia

e-mail: izidor.hafner@fe.uni-lj.si

It is well known fact that the triacontahedron can be decomposed to 10 prolate and 10 oblate rhombohedra. In [2] we found a dissection of two rhombic dodecahedra to a cube, and we simplified the construction in [3]. Here we give a decomposition of the triacontahedron to six halves of rhombic dodecahedron of the second kind and a cube. Decomposition of rhombic dodecahedra and the cube give a (1 x 1 x 2.5)- rectangular block. We can use Hanengraaf’s construction to get a cube [1, pg. 237].
To see a (LiveGraphics3D) animation dubleclick the picture.

References

[1] G. N. Frederickson, Dissections: Plane & Fancy, Cambridge U. Press, 1997

[2] I. Hafner, T. Zitko, A dissection of two rhombic dodecahedra of the 2. kind to a cube

[3] I. Hafner, T. Zitko, A dissection of quarter of rhombic dodecahedron of the second kind to a cube