Equidecomposition of rhombohedron, hexagonal prism, and rhombic dodecahedron

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 that hexagonal prisms, rhombic dodecahedra, and rhombohedra fill the space [3]. Dissection of these solids to variety of other solids is also known [1,2]. Here we give a hinged dissection of the rhomohedron to the hexagonal prism, and hinged dissection of the rhombohedron to rhombic dodecahedron. The rhombohedron consists of the octahedron and two tetrahedra.

To make models, use the following nets:


[1] G. N. Frederickson, Dissections: Plane & Fancy, Cambridge U. Press, 1997.
[2] G. N. Frederickson, Hinged Dissections:Swinging & Twisting, Cambridge U. Press, 2002.
[3] R. Williams, The Geometrical Foundation Of Natural Structure, Dover 1972