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

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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.

Contributed by: Dan Suttin (October 2014)
With additional contributions by: Sándor Kabai
Open content licensed under CC BY-NC-SA

## Details

detailSectionParagraph

## Permanent Citation

Dan Suttin

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send