Example 6. Tetrahedron, hexahedron, dodecahedron and icosahedron with the same surface area, of which the volume is () (2008 national civil service examination paper).

A, Tetrahedron B, Hexahedral C, Regular dodecahedron D, Regular icosahedron

Conclusion: Geometric maximum theory:

1, in the plane figure, if the perimeter is constant, the closer to the circle, the larger the area.

2. In the plane figure, if the area is constant, the closer to the circle, the smaller the perimeter.

3. In three-dimensional graphics, if the surface area is constant, the closer to the ball, the larger the volume.

According to the conclusion, the closer the surface area is to the ball, the larger the volume is, and the closer the icosahedron is to the ball among the four options. Option d