Construction
A truncated octahedron is constructed from a regular octahedron with side length 3a by the removal of six right square pyramids, one from each point. These pyramids have both base side length (a) and lateral side length (e) of a, to form equilateral triangles. The base area is then a2. Note that this shape is exactly similar to half an octahedron or Johnson solid J1.
From the properties of square pyramids, we can now find the slant height, s, and the height, h, of the pyramid:
The volume, V, of the pyramid is given by:
Because six pyramids are removed by truncation, there is a total lost volume of .
Read more about this topic: Truncated Octahedron
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