本論文的目的主要在探討正多面體的體積及其相關主題。首先我們用尤拉公式證明恰有五種正面體,接下來我們求出已知邊長的正多面體之表面積、體積、兩面角,以及正多面體中心分別到每一頂點、每一邊及每一面的距離。由於在推導公式時需要用到與正五邊形相關的知識,我們也討論黃金比例與18度及36度的正弦與餘弦等,跟正五邊形有關的主題。
The purpose of this thesis is to study the volume of a given regular polyhedron and its related topics. We first apply the Eular’s formula to prove there are exactly five kinds of regular polyhedra, we next derive the formula of the volume, surface area, angle of two adjacent faces for a given regular polyhedron with the length of its edge is given. We also derive the distances from the center of the regular polyhedron to its vertices, edges, and faces. Some results about pentagons are needed in our derivation we thus discuss some topics related to pentagons such as the golden ratio, the sine and cosine of angles 18 and 36