What is the volume of this octahedron?

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Can anyone help me with his problem? To me, this is a hard problem.

What is the volume, in cubic centimeters, of a regular octahedron whose vertices are the centers of the faces of a cube whose edge measures 6 cm?

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Basic approach. Divide the octahedron into two pyramids. Use the fact that a pyramid, like a cone, has volume equal to one-third the area of the base times the height (altitude).