在此篇論文，我們想了解：如果在平面上給定兩個圓，我們找到不同的兩組個數相同的圓圈相切於這兩個圓，我們想了解，這樣的兩組圓圈是不是會有什麼關係？一開始我們先介紹在平面上的Steiner Porism，然後利用反演將它們延伸到球面上的狀況，我們知道：如果有一個多面體，它可以找到一顆球，使得球與它的邊都相切，這些在球面上的圓圈可以看成是那個多面體與球的交集，我們想要了解在球面的Steiner Porism長什麼樣子？一開始我們先介紹最特殊的圓圈大小相同的狀況，然後再利用反演介紹共軸的狀況，再利用反演介紹不平行的狀況，而在球面上的兩個不相交不平行的圓圈可以利用反演將其反演成共軸的兩個圓圈，所以在球面上的狀況我們已經幾乎討論完成了。

In this thesis, we would like to discuss Steiner Porism which describe characteristics of circles are tangent to two circles simultaneously. In the beginning, we consider the situations and characters on plane. and use inversion to extend over 3-dimensional space. On the sphere, circles are regarded as the intersection of the circumscriptible polyhedron and sphere. we are trying to return these circumscriptible polyhedron. There is not every polyhedron exists dual polyhedron, nevertheless, it can be constructed by particular methods.We make the standard type of Steiner Porism on sphere further convert to symmetrical distortion. Each moment of symmetric distortion is a coaxial case of Steiner Porism when it rotates around the z-axis. Finally, we try to construct asymmetrical animation that associated with generalized Steiner Porism. We emphasized the phenomenon in the patterns rather than a complicated proof. We use Cabri 3D to do the patterns.

Contents
0 Introduction 3
1 Steiner Porism on Plane 5
2 Circumscriptible Polyhedron and Reye's Conguration 16
3 Steiner Porism on Sphere 20
Reference 36

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