Saturday, 14 September 2019

List of the 880 Frénicle Magic Squares of Order-4

Complete List of the 880 Frénicle Indexed Magic Squares of Order-4


At first listed by type in 2011, the 255 magic tori of order-4 were later given additional index numbers in 2012. Then in 2018, it was found that the 255 magic tori came from 82 multiplicative magic tori of order-4. In 2019 some of the magic tori of order-4 were found to be extra-magic, with nodal intersections of 4 or more magic lines and / or knight move magic diagonals. Other studies of the magic tori of order-4 have included sub-magic 2 x 2 squares (in 2013), magic torus complementary number patterns (in 2017), and even and odd number patterns (in 2019).

It has become necessary to provide an easily accessible document that recapitulates these different findings. I have therefore compiled the following list of the 880 Frénicle indexed squares of order-4, together with their Dudeney types and details of the magic tori: