Fourth-Order Magic Torus Chart

The fourth-order magic tori have already been identified and classified by type in a previous article "255 Fourth-Order Magic Tori, and 1 Third-Order Magic Torus." The fourth-order magic tori have also been indexed in numerical order using normalised squares for convenient reference in the "Table of Fourth-Order Magic Tori."

The latest study below shows how the 255 4th-order magic tori are linked, and how they interrelate. The Fourth-Order Magic Torus Chart proposes the division of the 255 magic tori into 25 groups, and indicates the position of each magic torus in the system. All of Bernard Frénicle de Bessy's 880 4x4 magic squares, and all of Henry Dudeney's 12 square types are accounted for. A sample page of the Fourth-Order Magic Torus Chart is shown here:

New developments!

Posted on the 24th April 2024, a new article entitled "Plus or Minus Groups of Magic Tori of Order 4" demonstrates that the 255 magic tori of order 4 come from 137 ± Groups!

Although "Plus or Minus Groups of Magic Tori of Order 4" proposes an alternative way of looking at things, the "Fourth-Order Magic Torus Chart" is still a valid basic solution, and therefore remains available below.

Please note that when you click on the button that appears at the top right hand side of the pdf viewer, a new window will open and full size pages will then be displayed, with options for zooming.