Western Illinois University
How to Make a Geodesic Sphere263271031750To make a geodesic sphere, start with an icosahedron. An icosahedron is made up of 20 triangles, five triangles meeting at each vertex. Find the midpoint of each edge of the icosahedron. For each triangular face of the icosahedron use the midpoints of the sides and the original three vertices to form four triangles, as shown. Calculate the number of vertices, edges, and faces of the icosahedron. These numbers are shown in the table.Calculate the number of vertices, edges, and faces of the geodesic sphere.Vertices: The 12 original vertices remain as vertices. In addition, we get 30 more vertices from the midpoints of the edges.Edges: Each original edge becomes two edges. In addition, for each face we get three new edges.Faces: Each original face becomes four faces (as shown in the figure).VerticesEdgesFacesIcosahedron123020Geodesic Sphere12+30 = 4230x2 + 20x3 = 60+60 = 12020x4 = 80For the geodesic sphere two different lengths are used for the edges. The edges are in a ratio of 1.13?to?1. The 60 edges coming from the original icosahedron edges are “longs.” The 60 edges coming from the new triangles inside the original triangles are “shorts.”Need: 60 longs and 60 shorts.For the geodesic sphere some of the vertices have five edges (“degree five”) and some of the vertices have six edges (“degree six”). The original 12 vertices (which were degree five) remain as degree five vertices. The midpoints of the original icosahedron edges become degree six vertices. Therefore, there are 30 degree six vertices.Need: 12 vertices of degree 5 and 30 vertices of degree 6.IcosahedronGeodesic Sphere3463290381001905010795 ................
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