摘要
　論文一開始先介紹空間中物件對正多面體投影的定義，在此定義下，我們將討論在正多面體上投影與切割的關係。在第二章至第五章，我們用切割的方法做出正立方體在正多面體、阿基米德多面體、卡塔蘭多面體上的投影，並觀察其動態變化。除了動態的投影變化，我們還要探討如何用非切割的的方法去建構正立方體在多面體上的靜態投影。第六章我們將討論靜態投影的檢驗以及為什麼在某些特殊多面體上無法建構出投影。此篇論文投影圖像皆用Cabri 3D軟體建構，在http://apollonius.math.nthu.edu.tw/d1/g9521510/g9521510/thesis/index.htm 網頁中我們可以看到所有投影圖像的動態變化與詳細製作過程。

Abstract
In this article, we define a projection from a segment or a polygon to a convex solid and discuss the relationship between the projection and the pattern. Then, we use the pattern method to represent the cube projection on Platonic solids, Archimedean solids and Catalan solids, and observe their dynamic variations. We also construct the cube projection that consists of six same blocks without using the pattern method. Finally, we would explain why we cannot use the method to construct the cube projection on some special solids and how do we check the correctness of the static cube projection.
All of the graphic files are constructed by Cabri 3D. We can see all dynamic variations and the detail constructive processes of each projection in the following website: http://apollonius.math.nthu.edu.tw/d1/g9521510/g9521510/thesis/index.htm.

[1] http://sylvester.math.nthu.edu.tw/d2/patterns-on-solids/
[2] http://apollonius.math.nthu.edu.tw/d1/dg-07-exe/933260/new/new/3d.htm
[3] http://mathworld.wolfram.com/Projection.html
[4] http://en.wikipedia.org/wiki/Platonic
[5] http://en.wikipedia.org/wiki/Archimedean_solid
[6] http://mathworld.wolfram.com/DeltoidalIcositetrahedron.html
[7] http://mathworld.wolfram.com/CatalanSolid.html
[8] http://en.wikipedia.org/wiki/Map_projection
[9] http://en.wikipedia.org/wiki/Catalan_solid
[10] http://mathworld.wolfram.com/ArchimedeanSolid.html