A truncated octahedron has 24 vertices.
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Start with an octahedron in the form of a quadrilateral based dipyramid a regular octahedron is a special case of this). This shape has six vertices - chop these off so as to remove a quadrilateral based pyramid. You will be left with a truncated octahedron. It is an octahedron which has been truncated (shortened) by cutting off its extremities.
The answer will depend on how many corners have been cut off in the truncation process.
it has 12 vertices
An octahedron has eight faces. If it has 62 faces then it is not an octahedron!
It has 60 :)