Space Division—View Points of Pathology and Physics

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: sato-ik510@pref.miyagi.jp

(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