Not sure what "canonical" means in this context.  Half of algebraic geometry is called "canonical ring" or "fundamental class" or some other vacuous term.

Please consider Elkies [The Klein Quartic in Number Theory](http://library.msri.org/books/Book35/files/elkies.pdf) and in general the book **The Eightfold Way** is online.  In the translation of [Klein](http://library.msri.org/books/Book35/files/klein.pdf)'s original work we find this futuristic image:

[![enter image description here][1]][1]

Also in [German](https://eudml.org/journal/10142).  The translated version has improved images


  [1]: https://i.sstatic.net/DRigf.png