摘要
中文摘要 在本篇論文中，藉由3D動態幾何軟體Cabri 3D的製圖效果，呈現Platonic多面體：cube、dodecahedron、icosahedron、octahedron、 tetrahedron；Kepler-Poinsot多面體：great dodecahedron、small stellated dodecahedron、great icosahedron、great stellated dodecahedron和Archimedean多面體：cuboctahedron、great rhombicosidodecahedron、great rhombicuboctahedron、icosidodecahedron、small rhombicosidodecahedron、small rhombicuboctahedron、truncated cube、truncated dodecahedron、truncated icosahedron、truncated octahedron、truncated tetrahedron的對偶多面體，以及角錐體和雙角錐體與自身對偶的關係。另外，本文還介紹了Platonic多面體和Archimedean多面體的積木堆疊法，找出Platonic多面體和Archimedean多面體的基本組合塊，再藉由反射與對稱拼湊出Platonic多面體和Archimedean多面體。 在以下網頁可以清楚看到所有多面體的動態模擬與詳細的作圖過程：http://apollonius.math.nthu.edu.tw/d1/dg-07-exe/9521502/透過這個網頁，每個人都可以清楚看到操作多面體的變化和動態幾何軟體Cabri 3D的應用發展。
關鍵字
對偶多面體並列摘要
Abstract In this thesis,I would like to perform the duality of five kinds of solids：Platonic solids(cube、dodecahedron、icosahedron、octahedron、 tetrahedron)、Kepler-Poinsot solids(great dodecahedron、small stellated dodecahedron、great icosahedron、great stellated dodecahedron)、Archimedean solids (cuboctahedron 、great rhombicosidodecahedron、great rhombicuboctahedron、icosidodecahedron、small rhombicosidodecahedron、small rhombicuboctahedron、truncated cube、truncated dodecahedron、truncated icosahedron、truncated octahedron、truncated tetrahedron)、pyramids with regular polygon faces(triangular pyramid、square pyramid、pentagonal pyramid)、dipyramids with regular polygon faces(triangular dipyramid、square dipyramid、pentagonal dipyramid).In addition,I would like to find the basic block of the Platonic solids and Archimedean solids,then construct the solids by reflection and symmetry . The following website shows clearly the dynamic simulation and detail process of generating polyhedrons：http://apollonius.math.nthu.edu.tw/d1/dg-07-exe/9521502/