| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 105 === 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
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