Octahedron in Cube: Proving the Possibility

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I heard somewhere that the Octahedron can't exist in the Cube exactly.

Is this true? Can't I prove that the octahedron in the cube?

Intuitively, they seems true. But I can't sure.
 
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Your question is not at all clear.
 
Octahedron_in_Cube.png
I meant this. I heard that this octahedron don't exist. But...
 
You are both drawing something and telling us it can't exist. Doesn't that bother you?
 
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