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# Example 4: Symmetries of a TetrahedronDescribe the symmetries of a tetrahedron_ A tetrahedron consists of four equilateral triangles that meet at six edges and four...

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###### Example 4: Symmetries of a TetrahedronDescribe the symmetries of a tetrahedron_ A tetrahedron consists of four equilateral triangles that meet at six edges and four corners (see Figure 9.4). Besides the motion leaving all corners fixed call it the 0" motion we can revolve 1209 or 2400 about a corner and the center of the opposite face (see Figure 9.4a), or we can revolve 180? about the middle of opposite edges (see Figure 9.4b). Since there are four pairs of a corner and opposite face and t

Example 4: Symmetries of a Tetrahedron Describe the symmetries of a tetrahedron_ A tetrahedron consists of four equilateral triangles that meet at six edges and four corners (see Figure 9.4). Besides the motion leaving all corners fixed call it the 0" motion we can revolve 1209 or 2400 about a corner and the center of the opposite face (see Figure 9.4a), or we can revolve 180? about the middle of opposite edges (see Figure 9.4b). Since there are four pairs of a corner and opposite face and three pairs of opposite edges; we have a total of 1 (0? motion) +4x2+3 = 12 symmetries. It is left as an exercise to check that these 12 symmetries are distinct and that no other symmetries exist. Figure 9.4 Symmetric revolutions of tetrahedron  #### Similar Solved Questions

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