In 2D we can easily construct golden ratio in a plane. In this paper we discuss the occurrences of golden ratio in 3D.Use the characteristic of regular dodecahedron and regular icosahedron, it is not hard to find some relationship with golden ratio. There are four sections in this paper, for the first section, studying how to construct golden rectangles in Platonic solid by the characteristic of golden ratio of regular icosahedron. The second section discussed how to embed a regular icosahedron in a regular octahedron with five different ways. The third section discussed how to embed a regular icosahedron in a regular tetrahedron with three different ways .The last section, constructing some interesting polyhedrons which are relative
to golden ratio.
This paper presents the graphs by the software Cabri 3D, in the website, you can see the productions and the applications of 3D dynamic geometry.
http://oz.nthu.edu.tw/~g9621608

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