# 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)

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"Volume of the Regular Tetrahedron and Regular Octahedron"

http://demonstrations.wolfram.com/VolumeOfTheRegularTetrahedronAndRegularOctahedron/

Wolfram Demonstrations Project

Published: November 13 2014