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A regular octahedron is a solid with eight faces, all of which are equilateral triangles. It can be formed by placing together two square based pyramids at their bases.
What is the volume of an octahedron with side length \(1\)?
In the picture below, there are the \(12\) pentominoes. Is it possible to tile a \(6\times10\) rectangle with them?
Show how to tile a \(5\times12\) rectangle with the twelve pentominoes.