Ikuro Sato1* and Ryuji Takaki2
1Miyagi Cancer Center, Medeshima, Natori, Miyagi 981-1293, Japan
2Kobe Design University, Gakuen-nishimachi, Nishi-ku, Kobe, Hyogo 651-2196, Japan
*E-mail address: email@example.com
(Received December 8, 2008; Accepted November 2, 2009)
Abstract. Some basic properties of the space division are explained. As elements of periodic division of the 3-dimensional space, the Fedorov's parallel polyhedra are introduced, including the cube, the rhombic dodecahedron and Kelvin's 14-hedron. The concept of stability in space division is explained, which is connected to the mechanical stability of the elements. The high frequency of pentagons as faces of elements is noted, and its relation to the stability of space division is suggested. Finally, some examples of divisions in spaces with higher dimension are given.
Keywords: Space Division, Kelvin's 14-hedron, Fedorov's Parallel Polyhedra, Stable Division, Pentagon