 # 3D Mitsubishi Logo on Octahedron Requires a Wolfram Notebook System

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

If 12 small octahedra with edge length 1 are removed from the center of each edge of a large octahedron with edge length 3, then three rhombi are formed on each face of the large octahedron. This looks like the Mitsubishi logo.

Contributed by: Sándor Kabai (June 2016)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

A physical model of this arrangement can be made as follows: take an octahedron and place eight tetrahedra on its faces to form a stella octangula. Continue by adding 24 tetrahedra, six octahedra, and 12 octahedra. This results in a large octahedron consisting of 19 small octahedra and 32 tetrahedra. Since the large octahedron is made up of small octahedra, 19 octahedra plus 32 tetrahedra equals 27 octahedra. Simplifying the equation, 32 tetrahedra equals 8 octahedra, that is, 4 tetrahedra equals 1 octahedron, which is yet another way to show that the ratio of the volumes of an octahedron to a tetrahedron is 4.

Here is the original Mitsubishi logo: .

## Permanent Citation

Sándor Kabai

 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