關於正多面體的星狀多面體，正四面體以及正六面體的星狀多面體並不存在。正八面體的星狀多面體是唯一的，名為stella octangula，它是由兩個正四面體結合而成。而正十二面體的星狀多面體共有三個。Coxeter 在1982 證明了正二十面體的星狀多面體共有58個。
克布勒多面體是由三個正十二面體的星狀多面體以及一個正二十面體的星狀多面體組成。
本論文透過3D動態幾何軟體Cabri 3D呈現出星狀多面體的幾何架構以及其作圖方法，總共分為四個章節。在以下網站中你可以很清楚地看到詳盡的介紹：
http://apollonius.math.nthu.edu.tw/d1/dg-07-exe/943204/Stellation/stellated polyhedrons.htm
透過這個網站，每個人都可以很容易地看到我的研究成果以及動態幾何軟體的應用與發展。

There are no stellations of the cube or tetrahedron . The only stellated form of the octahedron is the stella octangula, which is a compound of two tetrahedra. There are three dodecahedron stellations: the small stellated dodecahedron, great dodecahedron, and great stellated dodecahedron . Coxeter et al. (1982) shows that 58 icosahedron stellations exist (although Coxeter et al. include the icosahedron itself in their count, for a total of 59), subject to certain restrictions.
The Kepler-Poinsot solids consist of the three dodecahedron stellations and one of the icosahedron stellations .
This paper presents the design of Polyhedron under Cabri3D, interactive dynamic software of geometry. It is divided into four sections. You can crystal clearly to discover the detail in the website:
http://apollonius.math.nthu.edu.tw/d1/dg-07-exe/943204/Stellation/stellated polyhedrons.htm
Here you can see the production of this study and application of 3D dynamic geometry.

[1.] Wenninger, M. J. "Dual Models ", 1983, Cambridge University Press.

[2.] Williams, Robert, "The Geometrical Foundation of Natural Structure: A Source Book of Design ", 1979, Dover Publications.

[3.] http://www.ylmass.edu.hk/~mathsclub/ILC/Polyhedra/

[4.] http://mathworld.wolfram.com/Stellation.html

[5.] http://mathworld.wolfram.com/IcosahedronStellations.html

[6.] http://en.wikipedia.org/wiki/Echidnahedron