Abstract
We know that a rhombic triacontahedron can be dissected into 20 rhombohedra, and 10 of them constitute a rhombic icosahedron. Now, we want to dissect a rhombic enneacontahedron. We first use Platonic solid to create some special rhombic polyhedra, such as rhombic dodecahedron, rhombic icosahedron…, and then we dissect these rhombic polyhedra into rhombohedra. By observing the regularity of the dissections, we find that there are two ways to systematically divide the rhombic enneacontahedron. 1.Since any rhombic polyhedron is also a zonohedron, we can use the property of zonohedron to dissect the rhombic enneacontahedron into a smaller rhombic polyhedron. Therefore, we use the same technique repeatedly to dissect the rhombic enneacontahedron into 120 rhombohedra. 2.Depending on the faces of the rhombic enneacontahedron, we can divide it into many kinds of rhombohedral polyhedron which we are familiar with, and then dissect all the smaller rhombic polyhedra into rhombohedra. Finally, we still can the same result that a rhombic enneacontahedron can be dissected into 120 rhombohedra. We use Cabri 3D to accomplish our graphs.