# The Volume of the Regular Octahedron Is Four Times the Volume of the Regular Tetrahedron

The Volume of the Regular Octahedron Is Four Times the Volume of the Regular Tetrahedron

This Demonstration shows a visual proof that the volume of the regular octahedron is four times that of the regular tetrahedron through decomposition. The large octahedron has a side that is twice the length of any of the small octahedra. So the volume of the large octahedron is eight times as much as a small one. But the large octahedron is made of six small octahedra and eight tetrahedra. So the eight tetrahedra must have a volume equal to two small octahedra, and the ratio is 4 to 1.