Volume of the Regular Tetrahedron and Regular Octahedron

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Let be the length of an edge of a regular tetrahedron inscribed in a cube of edge length . Let stand for the volume of a solid . We get by cutting away four triangular pyramids from . The volume of such a pyramid is . Then . But these four pyramids form one half of the regular octahedron , which therefore has volume and the ratio .

Contributed by: Izidor Hafner (November 2014)
Open content licensed under CC BY-NC-SA




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