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.
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A truncated octahedron has 24 vertices.
12
The answer will depend on how many corners have been cut off in the truncation process.
an octahedron
An octahedron.