Kowalewski's Settlement Problem for the Rhombic Dodecahedron

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.

Kowalewski's diagram consists of 12 non-overlapping simply connected regions. Each region has four neighboring regions. There are also 12 two-digit labels. The Kowalewski settlement problem is to place the labels on the regions so that the labels of neighboring regions have exactly one common digit.

Contributed by: Izidor Hafner (August 2019)
Open content licensed under CC BY-NC-SA


Kowalewski's original condition is a little stronger. Two opposing neighboring labels must match the first digit and the other two the second digit. But if a solution with a weak condition is obtained, a solution with a stronger condition can be obtained by swapping some labels by exchanging the digits (e.g. 42 and 24).


[1] G. Kowalewski and D. Booth, "Construction Games with Kepler's Solid," Austin, TX: Parker Courtney Press, 2001. (Jul 16, 2019) www.zometool.com/content/KowalewskiWeb.pdf.


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.