Forma, Vol. 22 (No. 1), pp. 93-102, 2007
Original Paper

A Space-filling Three-dimensional Serial Polyaxis

Reachlaw Oka1* and Masako Kawamoto2

1Department of Surgery, Shiga University of Medical Science, Seta, Tsukinowa, Otsu, Shiga 520-2192, Japan
2Department of Social Welfare, Shuchiin University, 70 Nishi-jouuke, Mukaijima, Fushimi, Kyoto 612-8156, Japan
*E-mail address:

(Received November 3, 2006; Accepted September 5, 2007)

Keywords: Serial Polyaxis, Space-filling Curve, Fractal, Hamilton Path, Information Science

Abstract. A space-filling three-dimensional serial polyaxis analogous to the Peano- Hilbert curve, fractal recursion, the Euler path, and the Hamilton path is presented. A polyaxis is an object constructed by linear axes representing the object form and structural relationships, and is applied here to the construction of serial space-filling curves. A twodimensional representation of a three-dimensional serial polyaxis is also devised. The construction is consistent with the graph theory and object-oriented representations of objects, and involves seriality and recursion. The representation can also be readily extended to computational geometry applications and information sciences. It is shown that a closed circuit is not possible in spaces constructed by an odd number of units, where start and end points of the space-filling serial polyaxis must both be located in oddnumbered units.

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