The Square Model

From Zenodo —

The mathematical discipline known as finite geometry was founded by Gino Fano in 1892. In 1962, Hans Freudenthal said of the axiomatic approach used by Fano (and later by Hilbert), “The bond with reality is cut.” The diamond theorem  may be viewed as restoring that bond. It describes a group of 322,560 permutations, later known as “the octad group,” that now plays a role in speculative high-energy physics. See Moonshine, Superconformal Symmetry, and Quantum Error Correction .

The document below reproduces a statement, by Steven H. Cullinane, of the diamond theorem that has been in the online Encyclopedia of Mathematics since 10 May 2013.

Cite as

Cullinane, Steven H. (2021).
“The Square Model of Fano’s 1892 Finite 3-Space.”
Zenodo. https://doi.org/10.5281/zenodo.4718182 .

Another online version of the square model of PG(3,2) —