Volume of the Regular Tetrahedron and Regular Octahedron
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 .
"Volume of the Regular Tetrahedron and Regular Octahedron"
Wolfram Demonstrations Project
Published: November 13 2014