Maximal Unit Lengths in 3D

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

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

Put points in 3D space. What is the maximal number of unit lengths? For four points, it is obvious the maximal number is six unit lengths, using a tetrahedron. With five points, two joined tetrahedra give nine unit lengths.


This Demonstration gives the following best-known solutions up to 20 points.

If you can find missed solutions matching or surpassing the best known maximum values, please send them to the author.


Contributed by: Ed Pegg Jr and Thomas Rokicki (August 2016)
Open content licensed under CC BY-NC-SA



The distances shown here are actually to make the points friendlier.

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.