Abstract
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.