摘要

菱形十二面體一共有三個星狀多面體。第一個菱形十二面體的星狀多面體叫做Escher's solid，第二個菱形十二面體的星狀多面體可以藉由Escher's solid建構而成，第三個菱形十二面體的星狀多面體可以藉由第二個菱形十二面體的星狀多面體建構而成。外接第一個菱形十二面體的星狀多面體的最小凸多面體是cuboctahedron，外接第三個菱形十二面體的星狀多面體的最小凸多面體是truncated octahedron。這三個菱形十二面體的星狀多面體的相互關係將被整理在第六個章節。

在Cabri 3D下，這份論文將呈現菱形十二面體的星狀多面體的構造以及在動態幾何軟體下的相互關係，總共分為七個章節。任何人都可以清楚的瀏覽這個網站看出細節：
http://oz.nthu.edu.tw/~g943214/Geometry/Geometry.htm
在這裡任何人都可以看到菱形十二面體的星狀多面體和3D動態幾何軟體應用的關係。

Abstract

There are three stellations of rhombic dodecahedron. The first stellation of rhombic dodecahedron is Escher's solid.The second stellation of rhombic dodecahedron is constructed by Escher's solid. The third stellation of rhombic dodecahedron is constructed by the second stellation of rhombic dodecahedron. The convex of Escher's solid is cuboctahedron. The convex of the third stellation of rhombic dodecahedron is truncated octahedron. The relations of the stellations of rhombic dodecahedron are arranged in sixth section.

The paper presents the constitution of the stellations of rhombic dodecahedron under Cabri 3D Geometry, interactive dynamic software of geometry. It is divided into seven sections. Anyone could browse clearly to discover the detail in the wedsite:
http://oz.nthu.edu.tw/~g943214/Geometry/Geometry.htm
Here anyone could see the relations of the stellations of rhombic dodecahedron and the application of 3D dynamic geometry.

June 2007

Reference

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry

The Mathematical Gazette,Vol.41,No.337.[Oct.,1957],pp.189-194.

Brill, D. "Double Star Flexicube." Brilliant Origami: A Collection of Original Designs. Tokyo: Japan Pub., pp. 98-103, 996.

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 215-216, 1991.

Cundy, H. and Rollett, A. "The Stellated Rhombic Dodecahedron." §3.9.5 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 127-128, 1989.

Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, p. 36, 1983.

Jstor http://link.jstor.org/sici?sici=0025-5572%28195710%292%3A41%3A337%3C189%3ASOTRD%3E2.0.CO%3B2-D

http://140.114.32.1/~jcchuan/

http://en.wikipedia.org/wiki/Stellation

http://www.johnrausch.com/PuzzleWorld/toc.asp?t=_cat/il201.htm%23second_stellation&m=puz/second_stellation.htm

http://www.johnrausch.com/puzzleWorld/puz/seven_piece_third_stellation.htm

http://mathworld.wolfram.com/Stellation.html

http://mathworld.wolfram.com/RhombicDodecahedronStellations.html