WOLFRAM|DEMONSTRATIONS PROJECT

Maximal Unit Lengths in 3D

​
configuration number
-
+
57
points:
19
unit lengths:
66
Put
n
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.
points
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
lengths
9
12
15
18
22
27
31
35
39
44
48
52
57
62
66
71
solutions
1
2
8
26
5
1
1
1
2
1
4
8+
1+
1+
2+
1+
If you can find missed solutions matching or surpassing the best known maximum values, please send them to the author.